This is the second pic in a little series I made to sum up the fighting styles I associate with each of the main species in MLP (full list: fav.me/dcab8b3)  
Having done a few pics on the matter I think it’s rather clear that I think Mixed Martial Arts (MMA) is a good fighting style for Dragons. I based this one on a moment from the episode School Daze pt. 1 because it gives me a way to explain the Changelings as well (for those not aware the red haired one is actually a shape shifter) since I don’t really associate any style with them specifically but I do think they could use the style of whatever they turn into. Also, Ocellus is my favorite of the cast of students and I wanted to include her.  
I don’t own these characters just the pic