The tail/fin has pin sized holes and is starting to get shredded. The fin may even split in half. The edges of the fins are red, black, white, or clear. It will be hard to identify it on a butterfly(betta), and other bettas with the same colored fins. Black bettas are an example of a color hard to find fin rot on. Fin rot is caused by bad water quality or high ammonia. Ammonia levels should stay around 0, as 8 and over is super toxic. This illness can be cured by keeping the water temp around 80 and cleaning the water more often. Adding 1 teaspoon of AQ salt per 2.5 gallons will help also. Some cases the fin rot will eat the whole fin and work on the body. This will cause you to have to Euthenize(I spelled it wrong...) him. Preventing finrot is easy, you need to keep ammonia levels down (cycling recommended) and remove any thing that will hurt him such as plastic plants. That is all I know.
He probably doesn't have it