Have you checked the google play store to make sure the Amazon app is up to date?
If it is, try going to:
Then clear the cache and restart your device. If that doesn't work, go back to the above, and clear the cache, clear the data and restart. If you clear the data you will have to sign back into your account again; personally I would clear cache and data to start with and then restart, but I didn't want you to be mad if you had to sign back in.