I have a Kindle Fire first gen, and on that it's possible to tell it to allow apps from places other than the Amazon app store. So if I were you I'd check to see whether you can still do that (a Google search should turn up instructions) and get the app from Google Play.
This isn't really a question for Garmin, anyway. The Android app exists, and it's Amazon that's made the choice not to have it in their store. So you might want to ask them to put it there, or at least why they won't.
