Amazon recently updated their app and now it works on my Nexus 9, unlike before when it was called Amazon Instant Video and the app wasn't compatible with Nexus 9s running Lollipop.
And I'm not talking about the Google Play version of Amazon Video. I'm taking about the Amazon Video app found on Amazon Underground.
If so, how's the UI and functionality?
Side loading No longer working after update of Amazon video
You can sideload it on the Shield, but I think you might need a mouse.
I just use PlayOn. This also needs to be sideloaded, but doesn't require a mouse.
You can actually sideload the new mobile version on the Nexus Player and browse the UI with a remote. There are just a couple of places where it's fiddly, but otherwise it looks quite decent (it renders the tablet layout fine).
But actually trying to play anything crashes the app. I suspect it's because of the (ARM) libraries from VisualOn that Amazon uses for the player. The good news is that VisualOn have just announced new support for Android TV, so we'll have to see ...
No there are janky workarounds but the bottom line is amazon refuses to support it on anything other than Sony tvs. While they will say that they "Please be informed that we are working to expand our Amazon Instant Video service to a broader selection of devices in the future." They actively break functionality on the Sony tv app when someone extracts it and flat out refuse to release the roku app in the UK.
I contact them via chat every few months about Chromecast/AndroidTV support, and would recommend that every prime member do the same.
You have to google cast mirror it from your device (android, windows, mac, linux, chrome os). Or use playon.
It works in Sony TV s but is blocked on all others.