Jack Kent Cooke's silver Super Bowl trophy hadn't even had time to develop a spot of tarnish before he was hitting up the District for a brand new designer stadium. Specifically, what he wants is a domed stadium, preferably seating 75,000, which the city would finance by picking up more than $100 million in indebtedness. If he gets that, he says, his Redskins will continue to play football in Washington.

If he can't get that, he says, he will find a place in the suburbs for his team to play.

So there.

The Redskins' lease at RFK Stadium expires after the 1990 season, and Cooke's been talking about wanting a new stadium since August. At that point, he invoked civic pride: "The area deserves a far better facility than it presently has. It deserves to get into the swim of big cities regarding stadiums. It seems to me we are bringing up the rear."

Cooke, however, is a businessman who says he's been losing money on the Redskins. RFK Stadium seats about 55,000 and is the third smallest in the National Football League. If he could sell 20,000 more tickets a game, he could make lots more money. If he could sell luxury skyboxes, he could make even more money. And if he could get a piece of the action from the food and parking concessions -- which he doesn't get now -- well, he might be able to make ends meet.

Forbes Magazine listed Cooke as the 49th richest American last year, with a fortune estimated at $600 million. If he made only 10 percent a year on his holdings -- a modest investment goal -- he would be making $60 million a year just for staying out of trouble. He is not only rich, he is also colorful, audacious and predatory.

He has said he doesn't plan to move the Washington Redskins to some other city if Mayor Marion Barry can't meet his demands. What he is doing, however, is chatting up suburban officials to see if they will give him his designer stadium. But these days, suburban officials don't have visions of growth and economic prosperity when they think about sports complexes. They have nightmares about traffic jams and overdevelopment -- and losing their jobs.

So far, the city has bitten (or gotten bit) to the extent of hiring consultants to explore the feasibility of building a replacement for RFK. Cooke is saying he won't pay anything toward a new stadium. This from a man who paid $42 million in 1979 -- when $42 million was still $42 million -- to terminate his contract with his first wife.

Cooke, like a lot of hugely successful businessmen, is fueling an enormous ego. He owns not only the world champion football team but also one of the legendary horse farms in Kentucky. Now he wants a designer stadium, just like Joe Robbie, the Dolphins' owner, has in Miami. Only, Cooke wants to get it the way most hugely successful businessmen get things, namely by using a currency known as OPM -- other people's money.

And he's not above using appalling tactics to get it. Thus, within a week after the Super Bowl he tightens the screws on the city with a carefully orchestrated presentation of his demands in the media, twinned with a proposal from some Loudoun County developers for a privately financed "Ultra Dome" complex near Dulles International Airport. Perhaps, instead of skyboxes, the Jack Kent Cooke Memorial Stadium -- which is, of course, what it would be called -- would have "ultra boxes" as well. There's no subway stop near the proposed site, so, barring a breakthrough in transportation, it would probably also come complete with its own ultra jam.

This is the kind of strong-arming one associates more with gangsters shaking down a bar than with a legitimate businessman trying to do business with a municipal government.

The District is in no financial position to underwrite an extravagance such as Cooke proposes. A city that can't maintain the physical plants in its public schools has no business subsidizing a football stadium for its local millionaire. This is a city that has one of the the highest infant mortality rates in the country. The homicide rate is about to make it the murder capital of the country. Drug wars are breaking out within sight of the Capitol. Adolescents are carrying guns and trafficking in narcotics. It takes more time to get into public housing than it takes to get out of Lorton on a murder rap.

The best thing that can be said of Cooke's scheme is that he is going to force taxpayers and city officials to examine what's important, and to realize that until the social needs of the city are met, any talk of public financing for a sports stadium is a terrible distortion of priorities. Cooke obviously doesn't understand that.

RFK Stadium was named for someone who did.