Amazon Fire is not an officially supported device. However, you can still use it on most Amazon Fire devices, if you have Google Play Store installed. On all Android-ran devices (which Amazon Fire is), the app is distributed through Google Play Store.
Here is a handy guide on how you can install Google Play Store on your Amazon Fire, which will enable you to download all Android apps (including AmblyoPlay) to your tablet: https://lifehacker.com/how-to-get-google-play-on-a-kindle-fire-and-install-any-1790706649
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