Watch Amazon Prime on Apple TV – AppleTV 4 Jailbreak (appletv4jailbreak.com)

There’s are two easy ways to watch your Amazon Prime video content on your Apple TV using an iOS device.

The official Amazon Instant Video App supports AirPlay. The requirements are iOS 6 or later and an Apple TV from the 2nd generation or later.

All you have to do is:

Download the Amazon Instant Video App (App Store) and sign in with your Amazon Account
Start the movie, click the AirPlay Icon and choose your Apple TV as destination

The video should be now playing on your Apple TV.

Another way to stream your Amazon Prime Movies directly to your TV is an HDMI Adapter (there’s no Apple TV necessary!).

You need an Lightning Digital AV Adapter (Apple Store Link) and an HDMI cable.
Connect the cables and adapter. Your display should be mirrored on the TV.
Download the Amazon Instant Video App (App Store) and sign in with your Amazon Account
Start the movie (your iOS doesn’t show the video – instead you can see it on the TV)