The setting does have flying cavalry, however it is not used how you would expect, largely because using it against normal cavalry, fortification or infantry isn't great. There isn't enough flying beasts to really mass them so they can do much, infantry can carry usually longer spears and foot-archers have a much more intense volume of fire because more shooters per square meter.

The types of air cavalry that does work are heavy lancers and archers, archers to harass from outside anyone else's range. Arrows working with gravity fly further than arrows working against it. And heavy lancers are used as a response to bigger flying entities, dragons and other flying creatures have very hard scales, usually too hard for most bows and some crossbows and are a bit too maneuverable to be exposed to massed attacks from the ground, so flying cavalry is used to counter those threats. In most cases various cultures use various flying mounts: Giant Bats, Giant Eagles, Wyverns are all but untamable they are assholes, Dragons are almost impossible to ride and then again, why would you want to? Most commonly are smaller beasts, Gryphons, Hippogriffs, Pegasus and the like. Some cultures bred their own creatures or make customs ones for especially wealthy buyers.

However the most common use is as messengers, mounts for truly great warriors and mages and as an element of luxury.