You might check out Lee’s tuts here at the Cow, scroll this page:
https://forums.creativecow.net/cgi-bin/page_wrapper.cgi?forumid=2&page=https://www.creativecow.net/articles/script_gen/authorsort/brimelow_lee_script.html
After Effects and Flash-Part 1 by Lee Brimelow
also for small swf files,
Creating Simple Animations with Poser and Flash by Lee Brimelow
How to Create an Animated 3D Logo by Lee Brimelow with Swift 3D
Only one is specifically AE, but the long and short of it for AE is like Steve said, vector stuff only: text (dingbats and wingdingd are good), Solids with Masks, Effect>Render>AudioKeyframes (can be used like Stroke without an audio input layer, you can even change color over time, softness not supported), And Illustrator files. When you want to export, File>Export>Macromedia Flash (SWF), you get the Swf Setting dialogue box, just make sure Ignore is selected for Unsupported features and you’re good.
Now that flash has blurs and more, maybe the next version of AE will support these on swf export, hope, hope.
And there’s a really weird thing about Flash optimizing AE produced swfs, I just did a 5 sec, 640×480, 12 fps swf from AE with all the items above (Text, dingbats, AudioWaveform on a mask, masked Solid changing shape) and it came out at 173 Kb. Not great, but when that is brought into Flash, then Published (you need to change it from the default size if its large like my 640×480) out of Flash the size dropped to 10 Kb, no kidding, so don’t give up hope if the numbers look too big, run it through Flash to make it smaller.