There may have been a coolness when she was alive, but the British royal family turned out yesterday for the proper, brief funeral service yesterday for the Duchess of Windsor. The twice-divorced Baltimore socialite was an embarrassment to the royal family ever since her romance with King Edward VIII shocked the nation 50 years ago. All throughout her life she was not welcome in the royal presence.

But it was all proper yesterday. Her 30-minute funeral with no eulogies and no direct references to the 89-year-old Wallis Warfield Spencer Simpson, who died last week, was attended by Queen Elizabeth, Prince Philip, Prince Charles, Princess Diana, Princess Anne and the queen mother, as well as Prime Minister Margaret Thatcher, opposition leader Neil Kinnock, U.S. Ambassador Charles Price and the Duke and Duchess of Marlborough. Not at the service were Princess Margaret, Prince Andrew and Prince Edward.

Only 15 people, including the royal family, attended the burial at the family's private cemetery at Frogmore Gardens on the Windsor Castle grounds. The plaque on the casket said: "Wallis, Duchess of Windsor 1896-1986." It did not include the "HRH" (Her Royal Highness), the title the duke had unsuccessfully sought for her. She was buried next to the duke, who died in 1972, in the land she had privately said, "I shall hate to my grave."

Setting a Wright Wrong

It never fails. Just when you say someone was the only one or the first to do something, someone comes along to prove you wrong. So the Wright brothers were the first to fly. That's not what the state of Connecticut is contending. Gov. William A. O'Neill signed legislation yesterday asking the Smithsonian Institution to look into claims that a German immigrant flew over Connecticut two years before the historic Wright flight at Kitty Hawk, N.C., in 1903.

A group of aviation history buffs believes Gustav Whitehead made a powered flight over Bridgeport as early as 1901. They also claim the Smithsonian has refused repeated requests for a formal review of the contention that Whitehead made the world's first powered flight. O'Neill fell short of agreeing that Whitehead deserves the Wright brothers' place in history. He only believes the Smithsonian should look into the matter and said, "If in fact this flight did take place, then it should be documented."

End Notes

Francis Coppola is to be in town next month for the Washington filming of a major new movie titled "Gardens of Stone." Also expected to be here for the filming, beginning May 19, are stars James Caan; this year's Academy Award-winning best supporting actress, Anjelica Huston; and James Earl Jones. The story deals with the lives and sacrifices of military families during the Vietnam war. The filmmakers, through the Erickson Agency here, reportedly are looking for a new unknown actor in the Matt Dillon/Tom Cruise type for a major speaking role . . .

Famed film director Otto Preminger, who died last week at the age of 79, left his estate to his widow Hope, who lived with him on Manhattan's East Side. The size of the estate of the director of "Exodus," "Anatomy of a Murder" and numerous other films was given as "more than $500,000," a legal category that could mean it is much more than $500,000. The only other bequest was $15,000 to a niece, Justice Eve Preminger Friedman, a judge in the Criminal Term of the New York Supreme Court . . .

Jazz musicians and composers feel they have been snubbed at the Grammys, so they are planning to organize their own awards program. About 150, including singers Mel Torme and Sarah Vaughan, met in Los Angeles to inaugurate the jazz music academy with as-yet-unnamed awards. There is some talk about naming them in honor of one of the jazz pioneers, like Louis Armstrong or Count Basie. Plans are for the first awards ceremony, which will focus on lifetime contributions to jazz, to take place in the fall of 1987 . . .

Comedian Bob Newhart was in town Monday to speak at the U.S. Chamber of Commerce's annual national meeting in the Washington Hilton. Doing one of his phone call skits, this one between President Reagan and deposed Philippine president Ferdinand Marcos, he said, "Ferdinand, can you turn down the music? Do you have to play 'Brother, Can You Spare a Dime?' " Then he added, "No, Nancy never told the press about the 3,000 shoes" . . .