There isn't any specific prohibition against owning US jets AFAIK, but not many ever hit the market. WWII era stuff is common. Some of the early jets (e.g. F-86, F-100s, F-5/T-38) exist in private hands.
In general, the Russian stuff translates better to private ownership because there is much less specialized support equipment or maintaince required - in general the soviet's built stuff for a real SHTF scenario, where-as the US was much more willing to complicate the design to gain a small edge.
here's the kind of thing offered here : http://aircombat.com/about/our-aircraft/
fast and aerobatic planes, but not fighters.