If you are on android there is an, currently unreleased but usable, 2FA generator called "andOTP". In contrast to the mentioned Google Authenticator you can backup the entries with a strong password in an encrypted file. If you lost your phone you can install the app and restore it with the encrypted file. But don't forget the password :)
The app is available on the playstore and as well in the F-Droid store. If you are deeper in programming android or even java you can read the sourcecode on github as well or compile it on your own.
https://play.google.com/store/apps/details?id=org.shadowice.flocke.andotp