(posted in the amazon thread, but copied here for Android TV owners)
They don't have an app for android TV (probably due to them running the firestick, fireTV etc).
BUT...
If you have a Sony (2015+) android TV (and probably nVidia shield), grab the latest Amazon Video APK from apkmirror.com, install it from a USB stick, and enjoy originals in UltraHD and HDR without having to do anything except signing in.
DON'T FOLLOW THE BS RUNAROUND on XDA for "Prime Video Launcher". It's a bucket of fail.
It even shows as Sony Android TV in my registered devices.
Now back to the show! (notice the red circle telling you what quality it's running)