I did it and it works find
Actually, I don’t think that you did.
There’s no question that one can get the DCS App to install on a Kindle Fire. That’s very doable.
The difficulty is getting the in-app purchase of the Standard or Premium upgrade accomplished. One does not do this using the Google Play Store, rather, it must be done from within the app from the More.../Upgrade screen. When one does this on a Kindle Fire, the app cycles endlessly.