The Good and Bad
This reminds me SOOO much of Battle Chess for the old NES. I really missed that nostalgia.
There is a lot of good about this. The chess AI is very functional. You have all of the rules and they're all correct. The animations are usually pretty funny. I like the unlimited undo because it helps the player to see where they made their mistakes. Since it's optional, players looking for more of a challenge can just ignore it.
However, I do have some overall problems with this. First, I think as beginner's chess game, it might be just a tad too hard. However, for a more experienced player, it just gets kinda boring. I would equate the difficulty to about a 3/10 if you were playing something out of chess titans. Black plays very passively, I played a round where it took black 5 turns to play a non pawn, and even then it was a ROOK. When black is aggressive, it leads with it's Queen, and then I just get to chase her around the board. The computer also tends to not be able to handle standard openings very well, it makes relatively poor responses.
I'm not sure how limited Flash is with regards to this kind of program, it's very impressive with what you have done, but I think what would improve it is a difficulty scale. That way the people who are loosing too much can try and tone down the difficulty.
I also think that the Rules section might include some basic strategy tips for players. Discussion of forking, pinning pieces, discover check and the like would probably be very helpful to noobies.
Maybe it's just my eyes, but after staring at the board for so long, I tend to mix up the bishops in with the pawns, might want to make them just a little more distinct.
Finally, why no option to play as black? I mean, if you're going to play against a computer, it's nice to try and improve your game as black as well as white.
Overall, I'm just being kinda nit-picky with the bad, it's really well done and unique. Great job.