You can, but we strongly suggest that you continue playing on a non-Amazon device. You can do that (and keep your progression) by signing into Facebook on your Amazon device, and then, launch the game on your new device of choice where you will be offered to sign into Facebook as well. At that point, your progression should appear on your new device.
Find our game on Google Play Store: Link to the game
Find our game on Apple iTunes: Link to the game