Here's a tip by Chris R. on how to get Amazon Prime working on the Fire TV.
1. Go to Amazon's Account management settings.
2. Click on "Manage your content and devices"
3. Go to "Settings" tab.
4. Make sure current country is "United States".
5. Enter in a US address and save. (Google is your friend on this one.)
6. Reset the Fire TV to factory defaults.
7. Connect your new "US" Amazon Prime account to your Fire TV.
Please note: These steps may or may not work for you. Let us know if it works or if you have any alternative methods.
Thank you Chris R. for your contribution!