If you want to have user-level installs from Flathub instead of system-level, you can run
flatpak remote-add --user --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo
Then you should see an additional user option listed for flathub in the output of flatpak remotes.
$ flatpak remotes
Name Options
flathub user
Then you can use the --user flag with your installs as you were trying before, and it should work