For Amazon devices currently there is not a way to transfer your progress or data to another device. The data for this app is stored locally on your device. If the app is removed or deleted for any reason, all of the data and progress will be lost and it is not able to be restored.
For Apple devices, be sure to turn on cloud saving, so your progress can be stored and accessed seamlessly across devices.
For Android Devices, your progress will be saved to your Play Games account. As long as you are logged into your account on your device your progress should be available.