So I've attempted using ES Explorer to download 2 different apk versions of amazon video for android tv on apk mirror, the July update won't play any videos and the November update that was just released only shows up in a small box on the left hand side of the screen. Help appreciated.
I used this #sideloadtag and it works perfectly: PRMVIDLNCH
So to clarify for anyone in the USA reading this, if you have a Mi Box or Nexus Player and want to use Amazon Video, install the Amazon Prime Launcher (which acts as a front-end for browsing titles and then launches them in the Amazon Video mobile app on your TV). It will allow you to play videos in SD, but not HD.
If you have an Nvidia Shield TV, install the real Amazon Video for Android TV app that Amazon designed for use with Sony TVs. It will allow you to play videos in HD, but not UHD.
There's a link to xda on this sub for installing Amazon prime in shield. Worked for me.
The Android TV version of Amazon Video only works on Sony and Nvidia Android TV
Here's a homebrew workaround called Amazon Prime Launcher.