You'd think this was an easy question to answer, but the truth is the only current app for Android to play amazon video is a Google TV based app and I"m sure not many people, if anyone, has tried it. I know YouTube for Google TV works on the OUYA, so there's a chance.

TO answer the question, I don't think you can just play video on amazon instant in the browser. Like Hulu, they most likely block it.