Having a chase scene followed by a fight can handle a lot of conflicts in the air. The escape by plane in Indiana Jones and the Last Crusade? Totally chase rules. Mixing it up with the Red Baron? Well….
So, here's my thinking. A lot is going to depend on schtick, and in a lot of situations and for a lot of groups, just having it be a fight with special effects will do the job, but if I was Jim Javelin, Ace Pilot, I'd probably want a little bit more of an opportunity to show my stuff.
Most fictional dogfights aren't about making the shot, they're about lining up the shot. One plane is on the other one's tail ("On the dog") trying to catch him in his sights, while the plane in front maneuvers to get out of the way and, if they do something awesome, turns the tables on the guy behind them so their roles reverse.
There's a lot of conceptual overlap with the chase rules here, but that element of changing roles throws a monkey wrench in the works, because the chase rules assume that one side is chasing and the other side is trying to get away, a dynamic that is unlikely to change.
So in a dogfight, practically speaking, you're in one of three positions - behind, in front, or free-for all.
In a free for all (no pilot clearly in front or behind), both pilots maneuver to try to be the one to end up behind the other. This is a contest of Pilot skills, though each side should declare (in order of skill) if they're maneuvering, or taking position. Then roll off.
If there's a tie, the results are inconclusive.
If the winner was maneuvering, they may put a fragile aspect on their opponent or the scene (Something like "Coming out of the sun") to tag for free on the next roll.
If the winner was taking position, they need to have gotten spin (won by 3 or more). If successful, they are now behind, and their opponent is in front - let's call them hunter and prey just to keep it straight.
Once you have a hunter and prey, you can do this one of two ways.
Hunter may now make attacks, using guns, which the prey defends against with piloting. If the Prey ever gets spin on his defense, he breaks free, and the situation returns to a free for all.
For the hunter to take a shot, the prey must have an "In my sights" aspect on him. To do this, the hunter makes a maneuver against the target (pilot v pilot) to put the aspect on him. This is a fragile aspect with a success, though with spin, it lasts until the prey shakes the hunter loose (see below). Once the aspect is in place, the hunter may rolls guns and, if successful, damage the target plane (see below)
The prey defends with piloting and, on his turn, can try to shake off the hunter or maneuver. This works similarly to the free for all phase, with the prey declaring that he's maneuvering or breaking free.
If they prey is maneuvering and succeeds, he may add an aspect normall (or remove an "In my sights" aspect from himself)
If the prey tries to break free and generates spin, the situation turns back into a free-for-all.
Planes damage like people, boxes consequences and all. Biplanes are pretty fragile, so I'd give them only a small number of boxes - maybe none at all.
Minions can participate in the fight, each in their own planes. So long as one side has minions backing them up, they get a +1 on all piloting rolls. During a free for all, either side may declare that they're shooting at minions as their action, and if they win, the opponent loses one minion plane.
If, during a free for all, one side makes a break for it, we've just changed from a dogfight to a chase. Enjoy.
Vehicle stats have been posted for many prop fighters.