APK (ATVAndroidCleint.apk) is Posted:
Works on unrooted Gingerbread devices and force closes on Honeycomb/ICS when you try to go to a video's page. On rooted devices you'll need to install OTA Rootkeeper then force close and re-open the video app. You can also freeze/defrost it with Titanium Backup.
Option #1 to Log in to Your Amazon Account:
Open the Amazon video app and find a video you want to watch. Tap the orange box to buy the video and log in with your Amazon account. Once logged in the prices in the orange boxes should adjust if you have Prime and you'll be able to watch videos. If you get an "Error Linking Device" proceed to option #2.
Option #2 to Log in to Your Amazon Account:
From a Kindle Fire ROM dump obtain and install MyAccount-unsigned.apk and com.amazon.dcp.apk. The files in this post should work even though its not a complete ROM dump. Now you can associate your Amazon account with your device just like you would a Google, etc account. From Settings, Accounts you should be able to add an Amazon account. Now go back into the Amazon video app and you should already be logged in and able to watch videos.
If you still get a "Your device is no longer configured correctly to play Amazon videos" error try restarting your device after you temp unroot with OTA Rootkeeper. Some devices, usually running CM roms have had issues with the error even after temp unrooting.