It is very simple to add Yahoo mail to Google authenticator and for that,
- Go to the Yahoo mail app from the Home Screen of the device
- Now, tap on the User icon and tap on Settings
- There you will find the Manage Accounts option, tap on it
- Tap on the Account Info and then, tap on Security Settings
- Unlock the phone by using the credentials and tap on the button on the Two-Step Verification section
Doing this will keep your Yahoo account secured on the next level and if you think that there is some issue in your account then, Yahoo contact customer care service.