So much back and forth saying that Google and Apple actively blocking Amazon, that's not the case. As you can already instal the amazon app via the Apple app store, on the Google side you have to find the Amazon app store (now known as the underground store??) download the instant video app all the while having to essentially sideload Amazon apps to get them on your Android device. Ever since Prime video was released Android users have asked for years to have mighty Amazon give them a Prime Video app. Well, they got one but missing Chromecast support.
The process of adding Chromecast support is relatively easy from a dev stand point (layman's understand, not an expert at this) Amazon refused to do this. They only wanted to push their own streaming devices as the only way to view Prime video content on your TV easily.
All of this is on Amazon's shoulders. They only want you to buy and use their brand of content streaming devices to view Prime video. This will ultimately turn around and bite them as they try to pass blame off onto others and deflect bad press onto Apple and/or Google as ill informed public will swamp Apple and Google and demand them to play nice with Amazon.