It probably depends on whether you want to run it something like a board game or something more free form.
Assuming flying mounts then you would want to make sure they have Athletics and Acrobatics skills as well as the rider having a ride skill.
If the creature has normal INT then it can make its own decisions and has its own actions in combat. If it has Fixed INT then generally the rider has to tell it what to do so actively flying it will eat into the rider's actions.
Generally speaking, if your riders are firing at each other (crossbows, pistols, etc) then you would expect to suffer a total modifier of -40% (-20% for firing from a moving platform and -20% aiming at a moving platform.) They would fire on their actions as normal. If firing at a rider they may also be doing the equivalent of firing into cover.
However you can allow riders to make opposed ride tests as an action. allow the winner to gain a +10% advantage. You should have the ride skill capped by the mount's athletics though. Also give faster or smaller mounts a plus to the contest. Having an advantage simply reduces your negative modifier. The advantage may be height, positioning or what ever.
You can allow riders to keep making this test in order to keep increasing (or decreasing) the advantage but limit it to a max of +30%. You could also allow a rider to blow their advantage in a single attack to get double benefit. E.g. If you have +20% advantage you can add +40% to an attack roll (cancelling out the normal -40) for a single attack.
If you have intelligent mounts then they will do all this on their own initiative leaving the rider free to make pot shots. Mounts could also attack each other.
This is just a quick and dirty way of doing aerial combat that doesn't require new stats or counters and so on.
Other winkles: if your mount can hover then you can stay stationary and not suffer the usual -20% for firing from moving object.
Acrobatics. Used for fancy maneuvers. Can be used instead of dodge while flying (Fixed INT mounts have their skill capped by the rider's ride skill though.)