So the new update to the Amazon Kindle app is now accessible with VoiceOver. I have not used the app due to its inaccessibility and thus now have to learn a new app. Gee I really am upset over that one :). I have found a few Kindle books that I want and so now I can download them. You can not buy books in the app its self. You will need to go to the Amazon website and login with the same account you used when setting up the Kindle app. Now you can find Kindle edition books and send them to your device.
If you are looking for a guide to using the Kindle app on your iDevice using VoiceOver I would check out this free Kindle book. You can get it at http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Ddigital-text&field-keywords=B00CL5NIGU.