Flash is a proprietary format, and the folks at Macromedia guard it zealously.
So there is NO open-source Flash renderer. You have to use a Linux plug in, provided by Macromedia, that happens to work with Open source browsers like Mozilla and Firefox.
There *are* open-source libraries to help you *create* Flash files, but none to help you *display* them.
(If that's in fact what you're asking. You might instead be asking this: http://www.w3schools.com/flash/flash_inhtml.asp
Sorry .. PSM
What happened with that "Midnight slowdown"?
"Moho" is an excellent animation package for Linux. It also happens to generate Flash (among many other formats). It's not free, but it's VERY good and (IMHO) a bargain at $99.00. Check it out: