Like in dragon ball, people can just levitate and defy gravity to move freely through the air. What techniques, methods, martial arts, and principles would be the most practical in a battleground where you are free to move in all three dimensions of space? The flying speed is limited to the reaction and combat speed of the average human, but can be trained to reach higher levels
Pendulous, durable appendages.
The problem with flying martial arts is that flying allows the body to build up tremendous kinetic energy. Grappling and throws are impossible at speed. What is possible is impact. An impact imparts the same force to hitter and hitted and I assert here that "hitted" is the Queens own english.
Yes. The hitted. Hittee? In any case a hit is supposed to damage your opponent more than you, and because the forces are the same the appendage hitting must be more damage resistant than the part of the opponent that gets hit.
Hitting with a fist or foot at velocity will do great damage and also probably break the fist or foot. Hitting with a weapon would be ideal and something like a flail would be best because the impact is not transmitted back thru the handle to the wielder.
But I take from this it is a no weapons kind of thing. I envision the fast flying combatant striking with an open handed slap. Or better an impact from a part of the body which has no bones and which protrudes from the spinal axis to allow the impact. The kinetic energy of the hit will be dispersed thru this appendage and so do less damage. Various appendages can be envisioned and this could vary from individual to individual, leading to different combat styles. Going into a spin right before impact will pull pendulous appendages away from the body facilitating the hit and this will also look cool for the anime.
Depends on the weapons they are using. If they have guns, it might be a bit like fighter plane dogfight. If it's melee weapons, it might look a bit like a medieval joust. The combatants fly full speed at each other, then as they pass each other they try to swipe the other person with something sharp and pointy. If the fight is in an environment where there is very little space to maneuver, like inside a small room, it might even look like a fight between Neo and Agent Smith from the Matrix movie (except maybe without the sunglasses).