Yes — on Google Play
Amazon Fire TV has a Google Play listing.
App Store
On Google Play
Is Amazon Fire TV on Android?
About Amazon Fire TV
Your entertainment sidekick wherever you go. The Fire TV mobile app puts the Fire TV experience at your fingertips—whether you're on the couch or on the move. Discover & personalize your entertainment anywhere: Browse titles and get personalized recommendations. Search for movies, TV shows, and more across all you…
Amazon Fire TV is listed on both the App Store and Google Play from AMZN Mobile LLC, so you can install it on Android phones and tablets. The Play Store listing shows 100,000,000+ installs.