Adobe Flash program can utilize Adobe Illustrator graphics to make a Adobe Flash movie. So 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. Maybe also works direct copy and paste of selected vector objects between Adobe Illustrator and Adobe Flash applications.
Direct conversion of ai files into fla by one-click does not make sense. They are two completely different formats.