Fdroid OTP Authenticator, how to move accounts to new phone?
The app doesn't offer any feature to do this, as you can see from the issue log. That leaves with two choices


Using backup methods for only an app as discussed here Full Backup of non-rooted devices
If your  device is already rooted, using titanium-backup is a popular choice (amongst other such apps)


But I suspect your device is not rooted, so you have only one choice