The app is lacking though, in both AirPlay capabilities and streaming over a cellular network.
Amazon has come a long way with its streaming service over the last year and now Amazon Prime has come to the iPhone. The service has been available on the iPad for some time, but the update makes it available on smaller screens.
Although it's nice to see Prime available on another device, the service is still lacking in some of the functionalities that you might expect to be available in an iPhone app. Amazon Prime is unable to be streamed through AirPlay, and unable to be used through a cellular network – it's Wi-Fi or nothing.
Source: Home Media Magazine