Henry Kissinger set a fashion trend when he was secretary of state, and next week, during the inaugural festivities, a lot of the top participants will be wearing clothing with bulletproof lining light as nylon.

In the early 1970s, at the request of the Secret Service, the U.S. Army had the Natick Research and Development Laboratory in Massachusetts design a bulletproof raincoat for Kissinger to wear to the Middle East.

His coat was lined with Kevlar, a miracle fiber that will stop a .357 Magnum bullet at close range and is the foundation of the body armor now worn by at least one-half of the nation's policemen.

Kissinger's raincoat was the first VIP garment that was more than a bulletproof vest. Later, one source says he ordered a topcoat and other garments that could be worn on occasions when a raincoat would be conspicuous.

Former president Gerald Ford owns a golfing jacket with a Kevlar lining.

When Pope John Paul II visited the U.S. last year, a group of New York City policemen took up a collection of $500 and had the Point Blank Armor Co. on Long Island make His Holiness a bulletproof coat.

At least three state governors who will be coming to the inaugural have ordered Kevlar clothes. So have some of the superstars who are coming to entertain.

Vice President-elect George Bush recently returned a Kevlar vest sent him by a Washinton-area firm which recommended that he wear it jogging. Actually, Bush didn't need the vest because, according to a source involved in the development of Kevlar clothing, the Secret Service and other government agencies "buy everything they need" for Bush and others directly from the manufacturers.

A Secret Service spokesman declined yesterday to say if the major participants in the inaugural festivities -- Carter-Mondale and Reagan-Bush -- will be wearing Kevlar.

"We can't respond to any questions, just for security reasons," said Dick Hartwig. "It would be up to them to decide if they want to use them -- with our recommendation."

Former Texan governor John Connelly didn't want to come to Washington for a position in the Reagan administration, but he'll be moving here anyway.

Connally will be working about two weeks a month out of the Washington office of Vinson and Elkins, the Houston firm where he is a partner.

Connally, who lately has been working on international cases, will parctice general law here. His move, according to one member of the firm, is to help boost Vinson and Elkin's Washington office.

But the partner joked, "He's really moving because his Houston tennis game is just ruined with [Vice President-elect George] Bush and [incoming Chief of Staff James A.] Baker moving to Washington.

Connally plans to keep his house in Texas, but is looking for a town house or an apartment to buy or rent.

Bargain hunters take note:

The price of Carl Bernstein's co-op in Adams Morgan -- listed for sale at $495,000 for the past two weeks -- has been reduced to a mere $450,000.

"The apartment if fabulous, but we discussed it and the price was just too high," explained Debbie Doyle, the real-estate agent handling the sale.

The best features of the co-op, according to one viewer, are the three walls of windows and "a spectacular view of the Cathedral."

Bernstein said he is selling the apartment "because I'm considering buying another property in Washington." If that deal falls through, his apartment will come off the market.

Bernstein had the walls knocked out in what was originally two apartments in the Ontario to create 2,700 feet of space in the current apartment.

The apartment now has two bedrooms, a den, a very large living room that was originally two separate rooms and a Florida room with a dropped, stained-glass ceiling.

But the apartment isn't for show to just anyone and has not been entered on the Realtor's computer, according to Doyle. "It's a low-key listing because he [Bernstein] doesn't want it advertised. He doesn't want to attract all kinds of tourists." Doyle said she is now screening potential clients on the phone "to see if they have that kind of money" and the apartment is being shown only on certain days when Bernstein's housekeeper is present.