Generally, you can’t. You can only transfer them to a new phone by using export to generate QR code then add them to new phone like you would any other QR code.
However, if you do have root, you can. The talented authors from protectimus have documented how.
Rooting your phone is a bozo no no.
This is a more time and effort consuming way to transfer Google Authenticator key to the other smartphone. It requires you to have root access to the smartphones.
To extract the secret keys manually you need to give adb root access, this is easily done with an app like [root] adbd Insecure if you’ve got stock ROM. And in case you happen to have custom ROM you might already have the necessary root access adb, so no additional apps are needed.
Set adb onto insecure mode with the application or directly, connect the smartphone to your PC or laptop and copy the Google Authenticator databases to the computer using the commands.
This is the pathname:
adb pull /data/data/com.google.android.apps.authenticator2/databases/databases
After the file is copied you can open it and see the keys using these sqlite editor commands:
select * from accounts;
Now you have your secret keys and can add them to your new device.
Read more of their post on google authenticator backup. www.protectimus.com/blog/google-authenticator-backup/