Unfortunately, Apple seems to be in no hurry to add Amazon Instant Video to Apple TV. While the service may compete with iTunes, the same can be said about Netflix and Hulu Plus (both can be found on Apple TV).
We’re not certain why Amazon Instant Video hasn’t been added to Apple TV, but Amazon seems to be trying to add the service to as many devices as possible.
Until Apple adds Amazon to Apple TV the best solution is to mirror the video to your Apple TV using AirPlay Mirroring on a Mac or PC.
Mac users who have a compatible computer with Mountain Lion installed already have AirPlay Mirroring built-in.
If you have a PC or a Mac that doesn’t support AirPlay Mirroring, you can use AirParrot to mirror your computer to Apple TV. AirParrot can be purchased for $9.99. If you are interested in AirParrot make sure you use the free trial period to ensure the software works correctly for you prior to purchasing it.
Amazon iPad App
Another way to mirror Amazon Instant Video is by using the free iPad app. However, the app does not support AirPlay and if your iPad is jailbroken you may need to install the xCon tweak to avoid jailbreak detection. It is a less than ideal solution, but you can use AirPlay Mirroring on an iPad 2 or later to view your Amazon videos on Apple TV.
Let Apple Know
In some cases, Apple does respond to customer feedback. Since the best solution for watching Amazon Instant Video on Apple TV would be an Amazon app directly on Apple TV, please let Apple know by leaving some feedback here and request the feature.