I've been trying to backup my Kodi setup to my flash drive and copy it somewhere else without a luck so far and i found out that it's because the device does not allow to write on external disks. I came across this youtube video suggesting to use SD FIX application but it says error "Platform permission file is invalid, no WRITE_EXTERNAL_STORAGE entry found."
There should be a folder on the drive that says something "Android" or "Data". Inside of that you should be able to find a folder for Kodi, and Kodi can write to it. If you are using a different app to copy the data, same process but replace "Kodi" with the name of the app.