I am just starting to checkout the streaming process, but I think if you log into Amazon website on your Tab 2 and go to Amazon prime video streaming you should be able to download from there. Like I said earlier I haven't tried this yet I am still learning more about my Tab 2 everyday. Take it easy.
There are some options out there, I just googled it. I can't put a hyperlink in here, but I searched for watching amazon prime videos on samsung galaxy tab 2 and a video and some other forums showed up. I don't have prime, but I've installed their MP3 player through the Play store and it works fine. Sorry I couldn't be of more help.