Several companies (Pyro, Lindberg, ITC, and probably others) have made small plastic Constitutions over the years. One or more of them may have been somewhere in the vicinity of 1/350, but if so I'm not aware of it. All those kits are quite old, and pretty crude; building one of them to a standard comparable to a modern warship kit would be a big, uphill battle.
On 1/700 scale the picture is much brighter. A British firm called Skytrex (www.skytrex.com - click on "ships," then on "Meridian Trafalgar Series") makes a series of 1/700 sailing warships - British, American, French, Spanish, and generic. The American range consists of the Constitution, President, and United States,the only kit rendition of the U.S.S. Chesapeake I've ever heard of, and the Essex. (How about a diorama featuring the latter sailing alonside the Essex of 1943?)
I have the impression that these kits were designed primarily for wargamers, but they're nice scale models in their own right. I've bought only one, the Victory. It has a beautifully-detailed, cast white metal hull, with separate castings for the poop deck, transom, boats, boat skids, and anchors. The masts and yards are also white metal castings; my intention (if I ever get up the nerve to build the thing) is to replace them with wood or wire. (The white metal ones are mighty flexible; maybe wargamers would find that an advantage.) The sails are photo-etched brass. (Again, that's probably for the sake of the wargamers; I'd be inclined to make them from paper.) The shrouds and ratlines also are photo-etched brass - inevitably a bit out of scale, but not bad.
This little kit could be turned into a real show-stopper of a scale model. I would, in fact, describe it as one of the four or five best renditions of the Victory in kit form. (The others on my personal list: the plastic kits from Heller and Revell (with the Airfix one a close runner-up), and the wood one from Calder/Jotika.) Highly recommended.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.