I went ahead and got the subscription. And so for anyone who might wonder, I will answer my own question.
You can't access chess mentor through the chess.com kindle app. However you can visit the website and use chess mentor and it works just fine.
Also to watch videos you may need to download some additional software. This however is more the kindles fault because it seemed the kindle wouldn't play allot of videos. Plus the software is cheap or free anyway.
I am not sure if you can download the videos so you can watch them away from your wifi hotspot without blowing all your monthly bandwidth.
I have been using chess mentor since it first came out and really enjoy it. That is I like it for its own sake not just because it makes me a better chess player. If that makes sense.
But anyway I have the chess mentor 2.0 and several modules. I can't even install them on my windows 7 computer anymore so I assume I can not use them on my kindle.
But what about the new cloud version of chess mentor that you get with a diamond membership? I see there seems to be an ipad app. What about kindle?
Has anyone done this? If so how well does it work?