I had the same thing, sometimes black screen, sometimes Amazon logo, but nothing more, but it had been working earlier.
Tried everything, power off tv and waited, remote power button for 30 secs, but to no avail.
I also went to the amazon web site and cleared out all my amazon prime devices - notice this is NOT the same as you amazon devices (go figure!) and started all over again.
Eventually, I fixed the problem by doing all the above:
1) Clear out all entries on the amazon PRIME web-site
2) Turn off TV for 1-2 minutes
3) Turn on, and then hold pwr button down for 30 secs
4) Go to setting and RESET your network settings
5) Connect to a different network (you might need to use your phone temporately to generate a network)
6) Start the Amazon app. This triggered the "Select your location" followed by "Re-register app" screens in the app on the TV.
7) Enter correct location and code (provided by the web-site)
8) Then configure your network on the TV back to normal
THAT worked for me. I don't know exactly why all this is needed, but I guess the trick is to trigger a total reset/restart. Not everybody will need all this, but I was without Amazon for month with multiple attampts - finally today I hit touchdown.
All my other devices have had no problems - this is only a Samsung TV related problem (I have both Samsung phones and tablets with no problems).
This one didn't work for me. With TV on, I held power button down for 30 seconds. TV turned off, then back on, then menu bar came on and went back off. I let go of the power button and selected home and Amazon. Finally I got Amazon movies.
Same problem here (Kauai, HI). I have spent hours on the phone and chat with Samsung and also with Amazon Tech support. Today I was on chat with Samsung and after going through the same shut down, start up, sign in again, yada yada and at the end of the session I was told that Samsung was going to issue a software update to the Amazon Prime Video app in the next two weeks. Anyone else heart this?
So I have been having a similar problem with the prime video app, however the screen either is completely gray and if I select whatever the cursor is on and that will play but it's a total shot in the dark or selecting the app only gets a flashing "prime video" logo and nothing less happens. Any suggestions?