Transfer FreeOTP secrets to new device using iOS 11 Automatic Setup
This answer can help you if your device is jailbroken (I would rather comment, but I am unable to).

Using the Filza app, navigate to the FreeOTP data folder. Copy the .plist file that is in the root of the folder. This contains the (unencrypted) secret and other information necessary to add the secrets to the new device/installation.

Using the FreeOTP QR Code Generator website, use the data from the .plist file to generate QR codes and scan the QR codes with the FreeOTP app on the new device/installation.