Unfortunately, Amazon decided to not only disable standard Airplay, but it also went the extra mile and killed off Airplay Mirroring (usually the best way to get video from an App without an Airplay video option).
Nice to see Amazon finally coming to the iPad, but I am not excited that they decided to cripple it. I guess they want us to buy a Roku box? I would rather bring my Mountain Lion equipped laptop into the bedroom and mirror Amazon Prime from there, since (right now) it works without a problem.