Well, I think your best bet is to activate Windows Dreamscenes which has been removed from Windows 7 using a mod available
here. And then exporting your flash animation as .MOV format(the only video format supported by flash) and then convert it to something like .AVI or .MPG and then apply it as your background. That's it! Let me know if you are experiencing any problems through the way!
---------- Post added at 02:56 PM ---------- Previous post was at 02:55 PM ----------
Oh wait! Are you talking about an interactive application or a simple flash animation/movie?
---------- Post added at 02:58 PM ---------- Previous post was at 02:56 PM ----------
If you are looking for an interactive flash application to be your background, then you can also activate Active Desktop as it was in Windows XP, on Windows 7 using this guide
here and then follow
this guide.