@Valerie_Visser Does a Fire Tablet have a web browser? If so, you can run your app inside of a web browser. Just copy/paste the share link (“Users > Links > Browser link” in the editor).
If you can install Android apps, then the standard install procedure should (in theory) work. Of course, in theory, there is no difference between theory and practice, but in practice there is (Yogi Berra).
This is the tutorial I used for my fire tablet. lifehacker.com - How to Get Google Play on a Kindle Fire and Install Any Android App You Want How to Get Google Play on a Kindle Fire and Install Any Android App You Want lifehacker.com