Looks like it’s a manual process.
It also looks like no Jellyfin developer is creating the builds on Flathub and that some random member of the flathub community did it.

Whilst the devs provide instructions for all manner of install methods, the preferred version is definitely via docker.

If I were you I would move to podman. They are very similar but the big difference is that podman uses docker containers. Podman also runs as a local user just like flatpak