There are many ways to create Flash animations in Illustrator. One of the easiest is to place each animation frame on a separate Illustrator layer, and select the AI Layers To SWF Frames option when you export the artwork.
For a video on exporting SWF
files from Illustrator, see www.adobe.com/go/vid0214.
For a video on creating mobile content in Illustrator, see www.adobe.com/go/vid0207.
You can also go to Adobe Studio (http://studio.adobe.com) for tips
and tutorials on creating Flash animations.