Flatpaks are all containerized, its really nice. All in the same directory, glad that it worked! You can do the same for the Flatpak user data directories in ~/.var/app/.
Run the Flatpak app once, close it again, then the user data file structure will be there. If you delete the files you simply reset the app, its like Android, awesome.
And if you simply delete all the files and swap in your old files, it will be the same Flatpak app as on the old device.