My Hangouts had two email accounts associated with it. One stopped working. I tried deleting and re-installing Hangouts. I tried deleting and reinstalling the email account that was not working with Hangouts.
Now when I try to add this second email account to Hangouts, I get the error message that the account already exists on the device.
I did delete that email account and before adding it via the phone's accounts manager, I tried to add it from Hangouts. It then added it as an email account but not associated with Hangouts.