I would like to get my video and content to my television from my Android phone or tablet but the Amazon Prime Video app does not support Chromecast.
How do you cast video/content to your television from Amazon Prime Video app?
Short answer is: you can't. You can use a laptop (windows/linux/mac/chrome-os) with Chrome browser to cast. Or you can buy an Amazon-Fire hardware device.
Long answer: the "cast your screen" solution now seems to be broken.
Broken? Exactly how?:
So for android devices, I don't know of any way to cast from your Android device to a Chromecast.
Official directions from Google on how to cast your screen: https://support.google.com/pixelphone/answer/2865484?hl=en
The Amazon Prime Video app does not support streaming to Chromecast from the app.
However a less well-known feature of newer Android versions is the ability to "cast your Android device's screen and audio" to the television. Or to put it another way you can "mirror your display" from your Android device to the television.
The "cast your Android device" feature is supported for later versions of Android 4.x (I don't know what version exactly).
As of now, it is possible to cast the contents of that app using Miracast, provided that both the Android phone and the TV supports that. I know for sure OnePlus 5, OnePlus 6, Redmi 5A and Redmi Note 5 Pro and Sony Bravia (don't know model number) supports Miracast, but Motorola G4 Plus doesn't.
I have used Amazon Prime app on the four devices personally to cast them using Miracast. I used inbuilt cast option under Settings app to cast, instead of doing it through the app.
Note: It is also possible to cast Netflix using Miracast, though you won't get any video, but only the audio.