How do you cast video/content to your television from Amazon Prime Video app? 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?
2018-09-13 update

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?:


the audio plays from the TV screen
the video does not play form the TV screen (TV is black where the video should be)


So for android devices, I don't know of any way to cast from your Android device to a Chromecast. 

2017-12-12 Use the Android feature called "cast your screen".

how to use "cast your screen"


turn on your TV and Chromecast
make sure your chromecast/phone are connected to the same wifi
unlock your phone
pull down the "quick settings" drawer from the top
touch the "cast screen/audio" button
your chromecast should now display what is on your Android device's screen
open the Amazon Prime Video app
play your content on your phone and the audio/video will show up on your television


Official directions from Google on how to cast your screen: https://support.google.com/pixelphone/answer/2865484?hl=en

background

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).

caveat


The "cast your screen" requires your Android device to be on, screen on, unlocked
because "cast your screen" mirrors your android device 


the battery usage is high
the wifi bandwidth used is high (has to send the audio/video from the internet to your phone, then from your phone to the router, then from the router to the Chromcast)

the resolution on the television depends on your phone's pixel resolution
"cast your screen" can cut out for various reasons and does not seem to be as reliable as normal Chromecast