Less than 170 Aarakocra Simulacra (CR 1/8)

These creatures are from Storm King's Thunder (See How many simulacra can Sansuri's Simulacrum create? - apparently unlimited, given enough material components and days / spell slots.)

They have some javelins (30 / 120 ft range), but only +4 to hit vs. Harengon Brigands having +5, so their damage/round against AC22 is significantly worse than DanB's answer. They have a fly speed of 50. They can hopefully expose themselves to Frightful Presence (120 ft) with only a small amount getting fried, then let it wear off so they're immune for the day. Then, with readied movement + move on their turn (as in David's pegasus answer) to within 30 ft for attacks without disadvantage. IDK if they can then scatter enough for the dragon to not be able to move away and catch them all with one breath cone, though. If not all, most.

More importantly, like a normal CR1/4 Aarakocra, five of them can summon a (CR5) air elemental:

Summon Air Elemental. Five aarakocra within 30 feet of each other can magically summon an air elemental. Each of the five must use its action and movement on three consecutive turns to perform an aerial dance and must maintain concentration while doing so (as if concentrating on a spell). When all five have finished their third turn of the dance, the elemental appears in an unoccupied space within 60 feet of them. It is friendly toward them and obeys their spoken commands. It remains for 1 hour, until it or all its summoners die, or until any of its summoners dismisses it as a bonus action. A summoner can't perform the dance again until it finishes a short rest. When the elemental returns to the Elemental Plane of Air, any aarakocra within 5 feet of it can return with it.

Air elemental tactics

This is the standard CR5 creature, fly speed 90 ft, multiattack of 2x Slam +8 to hit for 2d8+5 damage. (Against AC22 without disadvantage, one Slam averages 6/20 * (2*4.5 + 5) + 1/20 * (4*4.5 + 5) = 5.35 damage, for 10.7 DPR for a multiattack.) If they're frightened, they can still Whirlwind for 3d8+2 damage (DC13 Str for half), so 7.8 average damage (saving on 3 or higher.)

9.8 damage per multiattack means ~51.03 elementals will take down an ancient red in the first round. 255 Aarakocra can summon 51 elementals, and do enough extra damage on their own to finish off whatever HP the dragon last est. Depending on tactics, in the worst case (the elementals end their turn next to the dragon and its breath recharges right away) all the elementals get one more Slam as an opportunity attack before the dragon moves and fries them all, with only 10% making their save to survive the breath. In which case 34.02 elementals, or only 170 Aarakocra, on average almost killing it with 3 slams per elemental. I think any other tactical developments will result in more average attacks per elemental before going down, such as elementals scattering again, but I'm not sure exactly how it would play out.

They're faster than the dragon by 10 ft, but without the legendary action for extra movement. Total speed per round in initiative (not chase rules) = 2x90 = 180 ft, vs. the dragon with 2.5x 80 = 200. Air elementals are immune to exhaustion, dragons aren't. So I'm going to assume they can get more or less whatever starting position they want, such as surrounding the dragon on all sides, so a breath couldn't hit many of them.

(I haven't thought about how best to coordinate this with the aarakocra, whether it's worth sacrificing any elemental tactics to have the aarakocra be able to swarm in and attack in the same round after it uses its breath weapon. Losing any one aarakocra from the group of 5 costs an elemental, so teams should stay grouped near each other, and maybe in the same direction from the dragon as their air elemental.)

Its average HP total is 90, just 1 short of the average 91 damage of a fire breath. (Its dex save is +5, so only 10% of them make the DC24 save for half and survive). With readied movement, they're fast enough to surround the dragon. They have resistance to bludgeoning, piercing, and slashing from nonmagical attacks, so it helps against any melee attacks but not against Wing Attack (which is mechanically a save, not an attack roll.) That seems dumb (especially with "attack" in the name), but RAW is RAW.

If most of them started 100 ft away, they could have 80 ft of movement left after attacking, to fan back out into a big cloud. (Otherwise the dragon moves away with a wing attack before its turn, taking an opportunity attack from each of them, but can then hit them all with a breath on its turn because they're all grouped up where the dragon was. Ones that save will still survive, but the wing attack damage makes it very unlikely for a low damage roll to let any survive that don't make their save, or a negligible number if you randomize their HP as 12d10+24 instead of all having 90.) If they gamble on the breath weapon not recharging on the first turn and stay in, the dragon can wing attack + dash to move 200 ft away even without its breath weapon, so only a few of the elementals could get within melee range with their own dash, to be able to make op attacks if the dragon keeps fleeing.

From opposite sides of the 20-foot cube occupied by the dragon, they could get back out to a sphere about 2x 80 + 20 = 200 feet diameter, using their remaining 80 feet of movement to go away from the dragon after initially surrounding it on all sides to make melee attacks. (Or 210 since they can be 5 ft away while attacking. Air elementals could enter the dragon's space without squeezing, but they wouldn't want to). A 90 foot cone AoE is 90 feet across at its widest point, but narrower before that, so it only hits a fairly limited number, probably well under half.

Rinse, repeat with surviving elementals. (One of them takes an attack of opportunity on the way out, which only misses on a nat1, using the dragon's 1 reaction. They're resistant to the physical part, but not the fire from a bite.)

The dragon doesn't have enough speed advantage to disengage and get far enough away that the elementals can't catch up by dashing themselves, even with a wing attack after its turn before the elementals' turn.

Elementals aren't immune to the frightened condition, so they might want to try to trigger Frightful Presence and retreat until it clears before coming in again, if they plan to stay near the dragon while it takes a turn. This will result in some losses, but I expect less than 50% so it's better than having them use Help actions. But the dragon can only use Frightful presence on its own turn, and only as part of its multiattack, not when using its breath weapon. So it won't come into play on the first turn the elementals move in to melee, only if they stay in and gamble on the breath weapon not recharging.

Honourable mentions: CR 1/4 flyers immune to fire:

• Metallic Warbler from Fizban's, 14 HP, fly 60, one melee attack at +4 for 4 damage (1d4+2).
• Ashen Flying Sword from Keys to the Golden Vault, 17 HP, fly 50, one melee attack at +3 for 5 damage (1d8+1).

They're fast enough to swarm in with a readied action plus movement on their turn, as in David's pegasus answer. But they don't have to be clever about it because they're immune to fire damage. However, a Wing Attack AoE will destroy them all with an average roll (17 damage from 2d6+10).