Adding the steps I took to make it work:
Note (1): If you haven't used the Fenix Livery Manager before, you can create the necessary folder structure by downloading any livery from the manager. This will create a folder called "fnx-aircraft-320-liveries" in your MSFS Community folder.
Note(2): I use MSFS Addon Linker and store my liveries on a different drive. GSX doesn't recognise this location even though it's active in the Addon Linker so for the moment, I've moved all my flightsim.to liveries from the custom directory to the default MSFS Community folder.
1. Download the livery you like from flightsim.to.
2. In the downloaded zip file, browse until you reach the folder called 'FNX_320_IAE_xxx'. In my case, it was 'FNX_320_IAE_VTTTM'. Copy this folder to the following directory: Community\fnx-aircraft-320-liveries\SimObjects\Airplanes.
3. Run FSDT Universal Installer and click on 'Config' for GSX.
4. Enable 'Fenix A320 B2'.
5. You should see that GSX recognises the livery and adds a 'model' folder into this particular livery directory.
6. If this occurs, congratulations, everything should work as intended and you can now close the FSDT Universal Installer.
IF GSX did not create a 'model' folder in the livery folder, chances are the ICAO airline in the 'aircraft.cfg' of the livery isn't recognised by GSX. In my case, this happened.
To resolve it, I changed the ICAO airline from 'VTI' to a more common airline such as 'AIC' in the 'aircraft.cfg' file and re-launched FSDT Universal Installer. This time GSX recognised the livery and added the 'model' folder.
So, it appears that if the ICAO airline in the 'aircraft.cfg' isn't known to GSX, it doesn't recognise that particular livery folder at all.
Hope this helps.