Linux 1-click mod installation appears broken in my experience. I only tested it on fedora. The installer appears to do everything well, but it doesn't register a mimetype. One way to fix it easily is to type in the terminal
gedit ~/.config/mimeapps.list
After this, you should add after
[Added Associations]
The following line:
x-scheme-handler/vintagestorymodinstall=Vintagestory_url_mod.desktop;
The following one-liner should work:
sed -i '/\[Added Associations\]/a \x-scheme-handler/vintagestorymodinstall=Vintagestory_url_mod.desktop;' ~/.config/mimeapps.list
I didn't test it on flatpaks, but if the desktop name is the same, it should probably work?