Amazon has just upgraded its Amazon Instant Video app for iOS. iPhone users can now watch movies and TV shows in HD on their phones, but they must have an Amazon Prime membership. Amazon has also added mobile data support for Amazon Instant Video as well. But I would assume most consumers would take better advantage of this upgrade using their iPad (or wait for the new one) or Apple TVs while using their 5GBps Wi-Fi speeds.
You can go and update (or download) the new Amazon Instant Video app in iTunes App Store now.