When you tap on the Clear Account Sign in Data button, the button becomes selected in green but nothing will happen. I am unsure if this is just a bug on Kindle Fire or if this is a bug on all devices because I only have a Kindle Fire. Someone in a youTube comments section said it happened to them on Android (im not sure what version), so that would be worth checking out when fixing this bug. 

I am not able to attatch screenshots because I can't transfer them onto my MacBook but i hope this description is good enough.