I had been wondering for a while if there was a particular file that housed all my favorites that i could backup and share between two computers. Today, i canceled a filtering process and it caused me to lose all my favorites which just moved this to the top of my priority list.

How can i backup my G'Mic settings/favorites?

I regularly back up the G'mic faves, so that I can use same settings on other machines.
In windows the G'mic favorites (gmic_qt_faves.json) are stored in:
C:/Users/"YouUserName"/AppData/Roaming/gmic

On Linux the path is user/.config/gmic

Normal procedure, copy your faves to USB stick or what ever media you prefer to use, and paste overwriting same file in the other computer.

thank you!