The flying ability doubles a unit's patrol strength and siege strength, making flying units particularly efficient for these roles. Flyers can also get a charge bonus when wielding lances, and cannot be charged by anything except other flyers.
Flying melee troops are usually scripted with Hold and Attack Rear to give time for enemy infantry to advance, leaving vulnerable archers and commanders exposed. In some battles, flyers scripted to attack immediately can have a decisive role through interrupting the scripts of enemy mages or thugs.
With good leadership, it is possible to script flyers to advance on foot in combat. Flying units set on a Line or Double Line formation, and scripted to Attack, Fire, or Hold and Fire (not Hold and Attack!) will advance on foot, rather than flying, once they have exhausted any ammunition you told them to shoot. This can be useful both for flying infantry who you'd prefer to serve as a stable front line, and for flying archers like the, who would otherwise bravely fly into melee with their Ice Knives when out of ammunition. This is not a panacea; the combat AI may decide to switch a squad in one of these formations to flying later in the battle.
When engaging in larger battles as a flying nation you should get used to mixing things up. Smaller squads of chaff can be used on many different orders (with or without hold, rear, close, largest etc) to hold units in place or otherwise disrupt the enemys plan before your bigger, often buffed squads jump in and attack. To get best coverage if you want your flying units to attack everything you put them on a simple attack command dividing the army up in more squads, this will provide a way better coverage than for example half of the army on attack closest and half on attack rear.
Most flyers trade poorly with similiar quality units or even province defense. The main bonus of flying in a battle map strategical way is the possibility to reach and kill commanders in an alpha strike, triggering a rout.
When fighting fliers against fliers it can be important to evaluate if you should attack directly instead of holding since this means you will get the alpha strike on the opponent if the opponent is on hold. Scouting is very important in a matchup like this.
The most common and easy measure against flying armies is blobbing up your army in a big pile with enough commanders to put almost all your commanders full of bodyguards.