One limitation of the flatpack package format is that is isolated from the rest of the environment so the setting to start as a background service may not be working for you. What I'd suggest is add this command inside ZorinOS's "Startup Applications". I've just installed and tested this myself and things seem to work fine.
Note that this will launch the program in full screen which you may not want. According to the project's documentation, you can also provide the --gapplication-service flag at the end of the command to run it as a service.
And btw you may notice from the link above that this project has actually been renamed to EasyEffects and it has its own package. It doesn't seem to be available through apt ZorinOS but there is one available as a flatpak, in case you want to give that a try.