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/
The flex SDK is located here: http://www.adobe.com/products/flex/sdk/ It looks like the documentation there is quite good, though admittedly I haven't used it much. Any text editor would be fine; I am currently using SciTE with these options files: http://arthurdick.com/projects/as3/
Regarding graphical stuff, SVG graphics can be embedded http://livedocs.adobe.com/flex/201/html/wwhelp/wwhimpl/commo...
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/