I would suggest starting with getting familiar with as3 first, as Seth mentions Essential Actionscript 3.0 is a great start. Then you would get familiar with simple graphics, physics and animation. Keith Peters has two great books that cover that (Foundation Actionscript 3.0 Animation and AdvancED Actionscript 3.0 Animation). This would be the a pretty good basis.
Then you would probably start lurking on sites like newgrounds, start looking for data structures and game optimizations. You would get familiar with more linear algebra, trigonometry, physics etc. and eventually learn more from outside the flash community.
Until then, you can find a a few more links to books and online resources in this similar question.
FlashGameUniversity might be a good place for quick start.
It also might be handy to follow people in the community and learn from they're mistakes/achievements and avoid reinventing the wheel later on. Changes are if you're aiming for the same thing as someone else (making great games for example), odd are paths will cross.
If you're not new to programming, you might want to do something 'painfull'. You might want to familiarise yourself with Flash, if only for a bit. That will help you a lot on the long run, you will understand the syntax better, because there will be also visual cues. You might collaborate with designers for assets/animations so knowing the best way to get the job done will be good. Using a decent actionscript IDE will be great, but make sure you got familiar with the Flash IDE too.
HTH,
George