If you want to use the football federation logo, just delete the 'nation' folder.
How to install Circle Flags in FM 22
Download and extract my flags folder and paste it in the following location:
My Documents\Sports Interactive\Football Manager 202x\Graphics\Pictures\Logos\Flags
Then open Football Manager >> FM Preferences >> Interface:
UNTICK "Use caching to decrease page loading times"
TICK "Reload skin when confirming changes in preferences"
Finally click Confirm and once reloaded the flags will now show in game.