It’s what ‘officially’ works for me.
You would have to make sure the Fire Stick on your TV is connected to the Echo device. I forgot what that’s called.
Keep in mind, my Ring was working when I posted this question - I had set everything up and saw it all work. But after leaving things alone for some time it would no longer work when asked to “Show the front door”.
If you’ve never gotten it to work in the first place you may be dealing with a configuration issue on your Echo device. Open the Alexa app and connect your Fire Stick to the Echo.