Sorry you're having issues with the Android app! Can you please let me know which version you're using? Have you tried going into your application settings, finding the Chess.com app, and clearing out the app data to see if you can log in after that?
Android app stuck at login screen
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I launch the app, enter username and password, get the little chess symbol that turns for a couple of seconds, and then... nothing. I'm back at login screen. Help?