Is it just sticking out more than the other one? And when he flares can you notice an obvious difference in the gill cover?
There could be several causes for this:
1. He has been exposed to other bettas/has gotten into a fight, leaving a damaged gill
2. Ammonia burns
3. Gill parasites
4. Water quality issues
5. Genetics
In the case of option 1, it rarely heals, but as long as he is active, alert and healthy, there shouldn't be anything wrong with it. As for option 2 and 4, can you tell us about your water params? As for option 3 you can treat flukes with Coppersafe, Formalin 3, or Permoxyn, and if you feel that it is gill disease afflicting him, Maracyn Two would work. As for option 5 unless it his causing him great discomfort, and making him sluggish/weak/tired, or giving him a lack of an appetite, it should be alright. Some bettas outgrow their genetics & change over time, and some don't. As long as it isn't affecting your little guy's comfort and well-being, there is nothing wrong with him.
Again, water params, tank size, tank temperature, water change frequency/percentage, and any noted behavioural changes would help. As would pictures.
What did you use to sedate him? Have you tried to block their view of one another (the male and the female bettas?) Does he flare very often? (24/7 or rarely)
Good luck