I have seen a lot of questions related to the Ring Doorbell and Kindle Fire...I figured out a workable solution:
Sideload the Google Play Store onto the Fire (I used the instructions at https://www.howtogeek.com/232726/how-to-install-the-google-play-store-on-your-amazon-fire-tablet/ )
Use the Play Store to install the Ring Doorbell app
Use the Play Store to install AutomateIt
Setup 2 rules in AutomateIt:
Rule 1: On notification from Ring, run the Ring App
Rule 2: On notification from Ring, run the Fully App with a 1 minute delay
AutomateIt will notify you that it needs permission to monitor notifications. Allow that permission.
Start Fully, ring your doorbell, see your front porch, cheer, wait another half minute or so, and Fully restarts, conduct victory lap...and profit.
If you have motion detection turned on for the doorbell, this will also show your porch if something trips the motion sensor.
Customer support service by UserEcho