Are you talking about what looks like a little flap of skin? If you are, then that's normal... my bettas have all had that... I think if the gill cover is sticking up or straight out to the side then that's an issue.
If you hold a small mirror in front of your betta where he can see it, he will see his reflection, and think it's another male betta, and flare up. You will see when he flares up that that flap of skin comes out (kind of like the dinosaur in jurassic park that opens up 'wings' behind his head and spits poison at Newman).
... he sure has pretty coloring, btw!
~Tara