I'm currently working on a flash game of my own. I didn't want to pay $700 for CS3 (or even $250 for flex builder,) so I'm doing so using only free tools.
I haven't attempted any complex graphics creation yet, but one program I'm looking into is Inkscape: http://www.inkscape.org/
I'd highly recommend the Tweener class for animations. I only recently discovered it, and it has made my life much easier: http://code.google.com/p/tweener/
The flex sdk contains a program called mxmlc, which is what I use to compile actionscript into the flash swf files. I did a search for an introductory guide, and found one I remember from when I was starting out. It's for the Windows version of flex, but I think it's pretty obvious what needs to be modified if you are using a different OS. http://www.senocular.com/flash/tutorials/as3withmxmlc/
..Actually maybe start over at the begininng :-) I have no idea how flash works or how one makes it.