Ever since Amazon Instant Video was available on Android, the most asked question from that qurter was, where is the Chromecast support. Of course it might take even longer for that support since Amazon is promoting it's own Fire TV. Leave it to the resourceful Android developers. Android Police is reporting of PrimeCast (nothing to do with Amazon Prime) an app that leverages Amazon backend services to pull together to show you a basic list of your purchased and rented movies and TV shows. The Amazon Prime Video users need to use the Browse tab and add individual videos to their watchlist as the app is unable to navigate list as yet.
Knowing how big boys operate, Amazon might close down the path but until then, all ChromCast users can use the app to expand their viewing span. My Chrome Cast sits plugged in to a TV somewhere, not used.