Well it depends on what exactly you want to do with Flash and the extent of which you want to use it. For example, you can use a web viewer in FileMaker itself and call an HTML page with embedded flash. If you want to build a front end with Flash then you will have to go another route.
The guys over at isolutions sepcialize in Flash/FM integration
Another alternative may be to use Flex. Soliant and Jeremiah Small have a library