I don't know about flash but I heard about one called Sai. A few artists use it. But not much else.

try Adobe Photoshop/Illustrator.

I use Adobe Photoshop for pretty much all my art. Painter is another good one, as is Open Canvas and Sai from what I've seen. Photoshop is pretty easy to use and find your way around, a personal fav, as well as there being loads of awesome tutorials around.

If you're just after something for animating, though, Flash is pretty decent. After Effects is also a good composition program, although it's harder to use and really is not for pure animation. If you get the trial of that, http://www.videocopilot.net/tutorials has some really good tutorials. You could even check them out first to see if you wanna bother with it. It's pretty powerful.

Good luck with finding the right program! (: