Hi @jack508!
Sorry to hear you're having trouble with your Fire TV.
To confirm your experience, does the Shuffle tile not appear in your station list or does it appear but doesn't appear to shuffle?
I've tested tried to replicate your experience on my Fire TV and I do see a Shuffle tile on my end.
In your post you mentioned signing out of the Pandora but can you try uninstalling and reinstalling the Pandora app on your Fire TV.
Let me know how it goes.
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