Have you got Maya 5? you can render it to vector using the new vector renderer. But if you dont , you could bring in a .mov , compress it in flash with its sorenson spark compression and then have that running in the background, though it would be pretty large in size to do that , unless its a small looping animation
There is also a vector exporter for Maya to flash (prior to 5) though from what I could tell from the site, it wasnt very good (and sadly the link escapes me now - though a search could bring it up no doubt)
lol, Link please, I never seen a export to flash from maya until Maya 5, It was asked in many sites, 3dbuzz , 3dpalace to name a few, and no one mentioned that there was one available. :-\