Here’s another method for getting the ST app to work on the Fire tablet: Amazon Fire 7 and SmartThings (Samsung login, Silk, Chrome?)
Download Chrome if you have not already.
Will open up smart things site in Silk
Click Options in upper right. (3 dots)
Click Open In Browser
Reopen Smart things
This takes you to site in Chrome to enter password.
Smart things now logged in.
I couldn’t get this to work. It still opens silk inside the SmartThings app. I can log into Samsung from Silk browser directly, but not when using the app.
Is your device registered to Amazon?
Pretty sure. I followed the guided steps when I set it up and haven’t rooted it yet.