I'm sorry you're having this issue with Prime Video!
Let's try clearing the cache and data for Prime Video.
Select Settings > Applications > Manage Installed Applications from the Fire TV menu.
Scroll down to Prime Video, then select Clear Cache and Clear Data.
After these steps, restart your Fire TV Stick and see if you can access Prime Video. Also try plugging your device into a different HDMI port, and make sure you are plugged directly into your television and not an HDMI hub.
I hope that helps! If not, please let us know which brand of television you are using with your Fire TV Stick so we can do some more research.