Looking over settings. You would need to remove group flairs in the group settings for Trust Levels.
Then setup the Trust Flairs in the Theme Component for each Trust Level you want flairs on and choose the position you want it to display on the Avatar. The Actual group flair choice in the user profile will not have any flairs to choose from unless a custom group has a group flare.
The theme-component I linked will only show flair from the Highest Trust Level the member has.