I can't help much, but I already got a hint:
In Android, you don't need storage permissions to read and write, as long as it's to an app-specific folder like
/Android/data/com.example
You only need that permission when reading and/or writing to another folder, such as with what the app you asked this question for, is supposed to do.
The option for enabling the Storage permissions is somewhere in the Android Export Settings under the Permissions headline. These permissions are named Read External Storage and Write External Storage.