I finally solve the problem, the issue was not either in Amazon's app or in Apple Tv, when I received the web authentication code from the Apple Tv to Amazon's Prime video, I opened my Prime video account ( in https://primevideo.com/mytv ) in the browser of my iPhone (safari with IOS 12.4.8) every time I sent the code to Amazon I received the message "An error ocurred, tray later". I tried to do the same authentication process in a PC (Windows 10 with browser Opera Versión:56.0.3051.43) with the same result, but here I noticed another messsage from the browser, site primevideo.com was trying to open an advertising add that was blocked.
So, I went to my iPhone, where I have installed the app 1Blocker Legacy to block advertising adds among other categories of non-desired pages and white-listed primevideo.com.
What I did was:
- Open 1Block
- Go to section CONFIGURABLE
- Open category WhiteList
- Add the URL: www.primevideo.com
Repeat the authentication processo for Prime Video
- Open the app (in Apple TV)
- Select section: Identify
- Get web code authentication (six letters and digitis)
- Open https://primevideo.com/mytv (in iPhone's Safari)
- Put my credentials for Prime video
- Write the code (six letters and digits)
- And Alas! Prime video started to work fine in my new Apple TV
It seems that Prime Video use a kind of advertising tag when process the web code, and my blockers interrupted the process avoiding to finish the authentication of my new device
