If you want to have your cycle as a seperate layer in your flash-animation, render out the animation as tga images (alpha included) take them into photoshop and convert them to png-files, import these into flash and trace the bitmaps one by one - this will convert them from bitmaps to vector described images, now you can click on the black background for each frame and delete it. It's takes a bit of time (depending on the amount of frames in your cycle) but it works!
There is also a script that renders maya-scenes directly to flash, but I haven't tried it.
Jeppe Nygaard Christensen
Ghost aps, Denmark