Yesterday I tried about a dozen of online chess providers (both "against human" and "against computer" functionality) and discovered that all of them (except ONE!) had one of the following two problems which prevented them from being usable on Kindle:
1. Written as a Flash animation. This is critical because Flash is not (and is unlikely to ever be) supported on Kindle platform.
2. A minor easily correctable glitch in the interface: instead of registering the move by clicking on a piece and dragging it to a new square, they should change the move registration to one of the following two methods:
a) click on a piece and then click on the new square it should go to.
b) enter algebraic notation (like "e2e4") in some entry box and then click on some "play" button or press "enter".
Ah, there were so many beautifully designed boards+pieces which looked GREAT on Kindle but, alas, were unusable due to this minor glitch.
Now the GOOD NEWS --- there was one provider which used BOTH of the abovementioned methods for inputting the move and here is the URL:
http://postcardchess.com/computerchess.html
I confirm that it works fine on Kindle 3. One minor inconvenience is that you have to reset zoom to 150% after each move (or play in landscape mode).