Jackie Kennedy asked Joan Braden to accompany her on an official trip to India in 1962. She did. She had met Jackie in 1960, when Bobby Kennedy told Braden she had better fill the Los Angeles Coliseum for John F. Kennedy during the presidential campaign. She did. But not before she was sure that Nelson Rockefeller, who had lent Joan Braden and husband, Tom, $180,000 to buy a newspaper in California, was not running. He wasn't.

These days Henry Kissinger spends every Christmas Eve at the Braden home, AFL-CIO president Lane Kirkland stops by on Thanksgiving, and recently Commerce Secretary Malcolm Baldrige attended the Bradens' 33rd anniversary party.

And now, Joan Braden -- political insider, Washington hostess, mother of eight, wife of columnist Tom Braden and a woman who still thinks of herself as a Kennedy Democrat -- has landed a $70,000-a-year job with a public relations firm run by a staunch Reagan Republican: Robert Keith Gray.

Braden's position with Gray and Company is the latest in a long list of interesting and influential jobs that friends and detractors alike credit to her social connections and force of personality.

Gray believes it takes all kinds in his business. "Yes," he jokes, "she is a Democrat, and that's her problem. I hired her because she has a great deal of credibility on both sides."

In the last 25 years, the 55-year-old Braden has had a career that is a Washington case study in the interplay of charm, power and survival.

She has zigzagged like a road runner across party lines: economic aide and personal secretary to Nelson Rockefeller; manager in both Kennedy presidential campaigns; television interviewer on WTOP in the late '60s; writer for national magazines such as McCall's and The Saturday Evening Post. And her most controversial job: consumer affairs adviser to the State Department in 1976, which raised eyebrows because of her family's friendship with then-Secretary of State Henry Kissinger, and because she did not appear to have the credentials for the job. Suspicions

One woman who demanded anonymity claimed there are mixed feelings about Braden's fast-tracked career. "Bobby Kennedy was a good friend of mine, too," said the woman. "But I never sold his name around town."

"Well," says Braden, "I bet that woman was never at my house for dinner."

Her latest employer, Bob Gray, who co-chaired the Reagan inaugural committee, is considered a very powerful friend to have in Washington these days because of his close ties to the administration. His thriving PR firm now claims to be the largest in town.

Braden will be one of 13 vice presidents, and in her words, "show corporate clients how to get things done in Washington." She will be given some of Gray's corporate accounts, and hopes to bring in a few of her own.

"I told Bob that the one thing I wanted to be careful about was . . . not to be hired on the basis of whom I knew or whom I could bring into the company because of my social contacts," says Braden, fingering her rings while sitting in the firm's Georgetown office, an airy refurbished warehouse called "The Power House."

"If I had more or less the same career I have had and lived in Dayton, Ohio," she says, "I doubt that people would think that I got hired because of famous friends . . . Because I changed jobs often, people tend to think of me more as a mother of eight and in terms of who comes to my house for dinner. I am touchy about the fact that I have something to contribute. I think having worked all of my life, I would like to think that I have abilities that are not dependent upon whom I know."

Braden's abilities are rarely disputed. If she has used her social contacts to get her foot in the door, as some have whispered, once inside she has proved competent.

"It would have been inconceivable for us to have found anyone with more access to people on the Hill," says William Rogers, who was Braden's immediate superior at the State Department. "She had the contacts. It was her secret weapon . . . her strong suit to start off. But when the issues began to come up, she mastered them damn well. She did her homework."

Now Braden is sitting in Bob Gray's office, surrounded by Reagan memorabilia. She flashes her famous cheerleader smile, her green eyes assuming the teal blue color of her blouse. A daily tennis player, she is tanned and slim. She has an aura of vitality and youthfulness, partly attributable to her children, now between the ages of 17 and 28. Her family's foibles and fun were the basis of the book and television series "Eight is Enough," written by her husband. The trouble with that, says Braden, is that at times "it was difficult for the children," because people would believe fictional scrapes were based on fact. "One episode had Elizabeth being arrested in a car for possession of drugs," says Braden. "She was only 14 at the time and at Georgetown Day School. Of course it never happened. You can imagine how all the kids teased her."

Braden talks openly and candidly, confiding enough to keep you interested but not enough to do herself damage. She gets sidetracked often, throwing out dozens of anecdotes about her days with Henry and Nelson and Jack and Bobby.

"I had told Nelson I would be for him in 1960 and in the meantime at Marietta Tree's in New York, I had met Paul Ziffrin who was California Democratic state chairman and he asked me to work for him," says Braden, with the enthusiasm of a 15-year-old talking about her first date.

"I said I couldn't, and Paul said 'If Nelson Rockefeller runs I'll work for him, but if he doesn't will you work for me?' And so on the day that Nelson announced that he wasn't going to run, Paul called me on the golf course. And that's how Bobby Kennedy came to ask me to fill the coliseum for Jack. And I must say I did do a good job." High-Powered Friends

What has intrigued many about Braden is her ability to move fluidly across party lines and travel in such high circles for so long without having a great fortune or experiencing a major social catastrophe.

In 1975, she threw a party for then-ambassador to Iran Richard Helms, "to cheer Dick up." At the time Helms was being investigated by the Justice Department for giving untruthful testimony to the Senate Foreign Relations Committee. The Democratic and Republican lions of Washington turned out in droves -- the Harrimans, the Symingtons, the McNamaras, the Kissingers.

"You know, when Tom and I came to Washington we were 21, the people we met were 15 years older," explains Braden of her high-powered friends. "We moved to California, and when we came back they were all ambassadors and secretary of state and senators. The fact was that we grew up with these people. Henry was not always secretary of state. I knew him through Nelson Rockefeller."

In 1976, Kissinger explained Joan Braden's allure this way: "She is always cheerful, extremely loyal, very warm-hearted and has been a steady friend."

"It's because in Washington especially," explains Braden, "friends need to be cared for and if you have that friendship for a reason, because you want to get something done and someone is a friend because he is a United States senator or because he is this or that, the friendship is very shallow . . . I have taken particular care with friendships so that they don't change with administrations."

Avoiding the press has also been a way Joan Braden has managed to hold on to her celebrity friends. Her parties, though frequent, are rarely covered by reporters.

During the Carter years, Braden thought Washington needed "some intellectual stimulation," so every two weeks the Bradens and then-British ambassador Peter Jay would host thematic, off-the-record dinner parties.

"We'd pick a current topic," says Braden, "like the Mideast, and it would be discussed off-the-record. I don't think the Carter people felt comfortable around the press, and this was a way to assure them it was not for publication. Republicans like Howard Baker and Paul Laxalt came, as well as Carter people like Stuart Eizenstat."

For the first time in more than a decade, Braden opened her house to the media last October for a party for her friend Bette Bao Lord. And that was to promote Lord's book. Again the lions of Washington showed up.

"It's very important that someone can come to dinner without having it known. When I have friends for dinner it's because I like them. You can't keep friendships otherwise." Friendships and Pain

These friendships, for all their glamor, have also caused Braden some pain. She took her worst flailing in 1976 when she was named to the $37,500-a-year State Department job. It was assumed by many in Washington that she got the job through cronyism. To this day, both Kissinger and Braden insist the secretary of state never knew his friend had gotten the appointment until he read it in the newspaper.

"It was awful," she says. "I mean there were cartoons with Henry pushing a baby carriage and me in it. It was embarrassing because I felt that I somehow was letting down my friends Nelson Rockefeller and Henry Kissinger. I only had one thought: that I am going to do this job and that I am going to learn more than anyone has ever learned."

One newspaper story, she says, "made it seem like I had wooed men in all administrations to get my jobs. Tommy Braden her then 16-year-old son said that night, when I went in to kiss him good night, 'You know, Mom, before I go to sleep at night I always think of the worst things and one of them is that I haven't worn my retainer and it'll cost more for my braces and the other is how am I going to explain it in school, my mom, a sex symbol.' So that'll give you an idea . . . "

She is asked if age-old rumors of her personal relationship with Nelson Rockefeller strained her marriage. She answers flatly, "No." She pauses, kneading her long, thin fingers together.

"Tom knows that I love him. I always did. We're not Catholics, but Tom is Catholic about divorce. He just doesn't believe in it. I had great strength knowing he felt that way. I don't believe that anybody can be with the same person for 33 years and not be attracted to someone else . . . It's not necessary for a man and woman to be monogamous, but there's no sense in hurting or embarrassing your husband either . The prerequisites for a happy marriage are not monogamy, but respect, trust and love . . . I'm more in love with Tom today than I was on the day I married him."

Her association with Nelson Rockefeller, she says, came at an impressionable time. She met her husband Tom through Rockefeller, and it was Rockefeller who lent the newly married couple $180,000 to buy an Oakland, Calif., newspaper, a sum they paid back with interest when they sold it.

"There was a time in my life when I thought if I didn't work for Nelson I couldn't do anything if he wasn't there to encourage me . . . And so I do miss him. I worked for him for eight years when I was very young . . . the first job I ever had," says Braden, and for the first time during the interview her chatter slows. "My sense of self-confidence was tied up in that job. Nelson thought I could do nearly anything. His death was an enormous loss. "

The other great losses in Braden's life were the Kennedys. "John F. Kennedy was my president," she says. "He came at exactly the right time in my life. He was a hero. Jack Kennedy was the first person whom I had known well and cared deeply about who had died. The death of both Kennedys was a deep blow to me, because I hadn't come to terms with death. I was with Bobby that night at the Ambassador Hotel . . . You don't forget those things."

Joan Braden's Washington has clearly changed over the decades. Many of her friends have died -- David Bruce, Alice Roosevelt Longworth, Stewart Alsop -- and many more are approaching old age. Her children, she says, keep her young. And life, she insists, "doesn't necessarily change because you've gotten older. I have just as many challenges in my life today as I did when I was 20.

"Maybe," she says with an infectious, playful laugh, "maybe what I am is a survivor. Maybe none of this is really glamorous or attractive but simply that I managed to survive."