That is a great question Gamenut. To run on the Fire it needs to be an Android app, so I'm guessing the answer would be "no" unless specifically made for Android. I'd love it though if it would
Edit: I found an answer at Amazon
It basically says to check the app store there by typing in Big Fish Games. However, you will not be able to use your credits with BFG to purchase games at Amazon.
I have 2 Kindle Fires and there are lots an lots of games available.