Amazon Fire OS is a variant of Android. The most important difference from a Playr perspective is that it does not come with the Google Play Store from which you can install the Playr app. Therefore you have to take a little detour to get your Fire TV setup to automatically play your Playr channel. To do so, you need a separate Android device (like a phone or tablet) to transfer the Playr app to the Fire TV once.
On the other Android device:
The app should now be transferred to the Fire TV, where you can find it in your apps section and start it. Now you can register the player to have it start playing your Playr channel. After this, every time the Fire TV is started, it will automatically start the Playr app with the configured channel.
After the installation, you don't need the Playr app anymore on your other Android device and we recommend you uninstall it right away to prevent it from automatically starting all the time.