Steven responded to this by writing a series of articles in his usual style discussing just how the US Air Force, and in a pinch the RAF, would do in aerial combat against dragons. It was his usual thorough discussion of how this particular weapon would do against dragons, just what the capabilities of dragons would be likely to be, whether the USAF pilots superior training would be effective, et cetera. Stylistically it was just like one of his discussions of how (say) the US marines would do against the Iraqi Republican Guard. Steven eventually concludes that
What I suspect that they'll discover is that dragon skin makes good shoes and belts, assuming they can find any pieces large enough to be used for that after all the shooting stops.
The follow-up articles, in which questions of more experienced pilots flying lower tech planes, Vietnam, dogfighting, air to air missiles, are even better, WWII in the Pacific, the transition to jets at the end of WWII, the manoeverability of the Mitsubishi Zero, and much more are discussed, all in the context of fighting dragons. It's all completely deadpan, and it is hilarious.
Of course, since dragons are mythical semimagical creatures anyway, it's difficult to guess what flight characteristics they might have. (As Bill points out in another email, strictly speaking dragons as described are impossible for several important physical reasons.)
Flapping wings have many virtues, but one thing they don't do is create huge amounts of thrust (i.e. comparable to a jet engine). The fastest winged creature in existence is a falcon in full dive, which can reach 200 MPH. No natural flier is remotely that fast in level flight. The wings of a dragon are not designed for high speed anyway; they would create tremendous turbulence and drag (if they didn't break off).
An A-10 Thunderbolt II (i.e. the Warthog) is rated 450 MPH. F-15's can exceed Mach 2 for short periods, and typically cruise at 600+ MPH. It is inconceivable that dragons would be able to fly at speeds remotely that fast.
Which means is that the jets would control the pace of combat. They can circle the dragons, come into them from behind, make slashing attacks and leave again, and then reform for the next attack. They can choose when to engage and when to run away, and they can engage when conditions are to their greatest advantage. If the dragon lands, they can strafe and bomb; if the dragon stays in the air they can circle and slash.
Or they can stand back and fire missiles from outside of firebreath range. The problem there would be coming up with a missile which would home in on a dragon, given that they're all designed to attack aircraft. Radar homers would probably be useless; a dragon is big, but it's also flesh (unless it's a bronze dragon heh-heh-heh).
Heat seekers are a different matter; if a dragon has firebreath, how warm is it? It's probably running hot anyway just because if its proportionately large volume relative to surface area. Still, it might not be hot enough to be detected by an AIM-9 Sidewinder unless that was recalibrated to look for a different kind of heat signature.
Which is why I think that it would mainly be necessary to rely on non-guided weapons. For fighters, that means their cannons, which is why the A-10 would be particularly effective. Its 30 mm GAU-8 gun is truly fearsome; it's a 7-barrel Gatling gun, which has a very high muzzle velocity which is added to the forward velocity of the jet resulting in monumental kinetic energy, specifically designed to pierce very heavy armor. I don't believe that even mythical creatures would be resistant to it.
In all there is about 5000 words of this. If you were trying to parody Steven Den Beste, it is hard to imagine a better effort, but he did it himself.