My tv has inbuilt Chromecast and a lot of apps have the cast option, but by far Prime video has the worst casting experience I've ever had. I try watching something and it gets stuck constantly, like it gets stuck every 20 mins into a movie and I need to close the app and try casting again. And it it just keeps buffering and maybe continue playing or else I'll have stop and try again, it's just a horrible experience overall.
No other app has these many issues when casting, it's like Amazon is forcing us to buy the firestick to get a better experience.
My tv has Android 8.0 and I tried side loading prime video but that also doesn't work as it constantly crashes and sometimes restarts the tv.
I don't understand why you're not just using the Prime Video app on your TV. If you prefer to browse for content on your phone or tablet you can cast it and then go to your Prime Video app on your TV and just select 'recently watched' to watch it on your TV without any of that fuss. The industry completely screwed up casting and it'll end up just like instant messaging, fragmented and mostly useless. I have a Nvidia Shield, and it has a Prime video app, I'm not at all certain whether or not such an app exist on embedded Android TV.