I have added a Ubuntu package for the Rhythmbox ListenBrainz plugin to the MusicBrainz Ubuntu PPAs. If you are using Rhythmbox on Ubuntu Linux 18.04 or newer you can install the package rhythmbox-plugin-listenbrainz from the MusicBrainz stable PPA:
sudo add-apt-repository ppa:musicbrainz-developers/stable
sudo apt-get update
sudo apt-get install rhythmbox-plugin-listenbrainz
Apart from Ubuntu you can also install it easily on Arch Linux from the AUR.
Currently there are no packages for other distributions available and I personally don’t have any plans to add any myself. I still hope my upstreaming attempt will get merged at some point. But if you feel like creating a package for this for any other distribution please go ahead, create one and let me know 