Since the Android TV leanback library is apparently compatible with SDK level 17, which is what the Amazon Fire TV uses, I set the minimum SDK level on my Android TV app and
It is definitely possible. However, there are a few things that you need to take into account.
First of all, the Fire TV does not honor the LEANBACK_LAUNCHER
intent filter, so you need to use the standard LAUNCHER
one. Moreover, you won't be able to see your application in the home screen before the app is actually published in the Amazon Store.
Other than this, you should not find many differences from, say, developing for the Nexus Player.
Here's a topic from the Fire TV documentation that might be helpful: How Fire TV Development Differs from Android TV Development.