Adobe Flash program can utilize Adobe Illustrator graphics to make a Adobe Flash movie. This means that your best bet is to import the AI file(s) and artwork to your Adobe Flash project library and use it in your flash project anywhere.
You can also export parts of graphics from Adobe Illustrator to a .swf or other common vector formats and import it to Flash project. And perhaps direct copy and paste method for selected vector objects between Adobe Illustrator and Adobe Flash applications works. Except for that, a direct ai to fla conversion seems highly unlikely.Open AI file Open FLA file
Multimedia platform used to add animation, video, and interactivity to web pages
Mac version of Flash development platform from Adobe