Thanks for visiting the Apple Support Communities, mclucia!
If we understand, you are using the Apple TV app on an Amazon Fire Stick, and you are only able to watch one specific episode of a single show. We see when you try to watch anything else, an error indicating in-app purchases aren't allowed pops up. You've come to the right place to get help!
According to the information below, found in Footnote 3 of Get the Apple TV app on your smart TV, streaming device, or game console - Apple Support, this is expected behavior:
"On Amazon Fire TV devices, you can't purchase content from the Apple TV app. You can purchase content on another supported device to watch it in the Apple TV app on your Amazon Fire TV device."
Cheers!