Vazandrew is not making a claim, he gave the answer very concisely.
"Amazon blocks the ability for airplay" meaning that Amazon has chosen NOT to allow airplay natively from the Amazon prime app/client that you may have on your devices. You probably can accomplish a 'stream' using Apple's native Mirror option but Amazon has "blocked' users from streaming Amazon Prime from within Amazon apps. They are likely choosing to do this in hopes that you would opt to use an Amazon FireTV hardware.
"...there are no plans for a native client." meaning that Amazon has no plans (known) to create a native app for use on AppleTV. They can develop one for Amazon Prime users to download but again i doubt they do, because they want you to use their devices.
_Skull - Apple would not be the ones to create the app to work with Amazon prime. It would be up to Amazon to create the app and make it available on the ATV platform. If you want it you should request it from Amazon.
Thank you Vazandrew for your efforts in the Apple community!