It depends a bit on how large exactly your flying creatures are. For example, if your pegasi are about the same size as a regular horse, but with wings I think they could be quite useful in urban combat situations. In the real world in particularly dense urban environments where your troops and enemies are quite close to each other (as in standing physically close, not that they're emotionally close and intimate) even helicopters are of limited use due to their large size and lack of suitable landing zones. For instance, I can picture pegasus-mounted snipers using their mounts to fly from roof top to roof top following their squad and providing sniping support. Or maybe even guys carrying heavy machine guns and using their pegasus to quickly relocate to where they're needed to provide fire support. Same goes with troops carrying mortars (as in the artillery) and anti-armor weapons such as the Carl Gustav Recoilless Rifle (or an RPG-7 if that's more familiar to you). Just to clarify, they wouldn't be fighting mounted on pegasus back but rather using the pegasus to quickly get from place to place to follow the squad they're supporting. Furthermore something like a pegasus would probably be a lot harder to hit with anti-aircraft guns or rockets than a helicopter due to its much smaller size, so they might even be preferred for troop transport in urban combat situations with heavy enemy fire.
Additionally, as others have already mentioned, they would probably be a lot stealthier than other options such as helicopters, and would likely be used frequently in stealth missions and other situations where remaining undetected is important.
Assuming your other flying creatures such as your griffons and hippogriffs are about the same size, then what I said about pegasi applies equally as well to them.
An important thing to keep in mind is to avoid comparing the creatures to aircraft such as stealth bombers or an A-10 "Warthog", as they would be fulfilling vastly different functions. Comparing them is like comparing a submarine to an aircraft carrier, yes they're both things in the water, but what they do in the water is completely different.
I think even comparing a dragon to military planes is misguided, as dragons would much more likely be used in a similar way to an attack helicopter rather than a jet fighter.
If you don't mind some advice, I think researching modern military tactics, particularly how different types of infantry are used and how the other branches support them could be very helpful, as I think that’s where the flying creatures would probably be used rather than the air force proper.