I have a hard time with the smell of tea tree oil, but have read that for people, at least, it's good for healing the skin. Someone on the forum was using it for shell problems a while back, I don't know what the results were.
Personally, I wouldn't use it "for maintenance." You said you recently got him, and your desire to make your turtle better as soon as possible is laudable. But, your turtle didn't get in the condition he's in suddenly and it will take time for him to show improvement. I'd let that amazing set-up and a healthy diet do their jobs first.
Flairing? Do you mean fanning (exposing himself) or fluttering (his paws at an object)?
"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-