From wot your saying you want to composite the image from Maya with the animation in Flash. Due to the exported animation being SWF based you are slightly restricted in your application choices.

Here are a few options:

Composite in After Effects, would need to be CS3 to work with Flash.
Save the Maya Image and use it directly in the Flash animation and export your swf out again, but you want it independant...
Try a composite in Photoshop CS3 also as it supports swf as far as I can remember, but this needs to be the extended version...

I would do a google search for free compositing tutorials and applications. There is one Mike McK recommended and it is good, but I do not know if it supports SWF Files. I think it was called VideoMACH.

Good Luck.