When Amazon finally released their instant video app for Android earlier this week i thought they had made my workaround post redundant. Alas, no, that hasn't happened.
I've tried the new streaming video app on a couple Android tablets and it really didn't work very well. In my experience the app crashed more and offered a lower resolution stream than the unofficial workaround (which required Adobe Flash and Dolphin Web browser).
With that in mind, I've updated my set of instructions on how to install the service, and added a section for the new apps - and left all the instructions for the unofficial workaround intact. I would recommend trying both, and using which ever one works best for you. Juli Monroe of Teleread thought that the official route was better, and it might be better for you as well.