You can Chromecast from any Android device.

I decompiled the app and pulled out a section that did the Amazon auth. The pop-up saying Amazon app store is not installed still comes up but when you hit OK it lets you log in and use the app.

Biggest issue is performance of the streaming. It stutters a lot. It is not due to buffering either. Looking at the code, they are using quick play (a service at&t just bought) and perhaps something called nexplayer. They pass in a parameter for forcing hardware acceleration. I tried removing that but the app wouldn't launch. I think they have settings server side that these parameters refer to.