Flatpak is a containerized framework by default.
It isnt usually supposed to be able to interact with the rest of your system… at least not in the same way as the more ‘traditional’ system packages.
That is but one reason that generally it is preferred to use regular packages over flatpaks & snaps.
For some more information see these:
Flatpak - ArchWiki
Filesystem · flatpak/flatpak Wiki · GitHub
Likely the filepath isnt exactly what you think it is.
You can maybe check more robustly using something like
ls -la /home/username
to see if your files are really there.
… I just begrudgingly installed flatpak and jdownloader to check … and checked. With download directory set to ~/Downloads (/home/USERNAME/Downloads) it worked fine, the files were accessible and deletable… now to delete it all again 
I will probably do this now:
flatpak uninstall org.jdownloader.JDownloader --delete-data
flatpak uninstall unused --delete-data
sudo pacman -Rns flatpak
##and it seems I need some extra cleanup manually:
rm -rf ~/.local/share/flatpak
rm -rf ~/.cache/flatpak
sudo rm -rf /var/lib/flatpak