I just spoke to someone from their Prime Video team and she told me that it is definitely an issue on their end and they're already working on fixing it. There's nothing you can do as a consumer, just wait. She said it might take up to 2 days but hopes it'll be fixed by this evening.
Thank you Miss V. Now we all know it's not US it's THEM. People can save themselves the trouble of restart, factory reset, and all these tedious yet ineffective measures. Let's give Amazon's engineer a day or two to fix this mess.
I'm having same issue on all devices both tv's and kindle, but not on my main computer. Like your selves have also checked settings and WiFi connection. Then tried main computer and it worked, so back again I went to try devices again same error message appears.