Once you do the handwaving needed to explain a modern-day world with flight-capable dragons in it, how would said dragons interact with the bureaucracy surrounding flying in the modern world? What sort of pilot's license would they hold? Would they get certified as an aircraft of some sort (perhaps in the Experimental category)? How would they display their registration? What would a checkride look like for them? How would they handle getting a medical certificate? What would annual inspections look like?
Update based on comments: think along the lines of a sentient dragon, with an average intelligence along the lines of the smarter end of humans, and the ability to speak and read English, although they may need a typist to handle writing/forms-filling. Keep also in mind that they'd be sharing airspace with human-built aircraft, as well as some infrastructure (I'd envision them as capable of STOL, but not quite VTOL -- but even helicopters need runways in certain cases).
Also, I was thinking they'd vary in size, but be no larger than a widebody aircraft, with RJ or bizjet-sized dragons much more commonplace. They'd be capable of high altitudes, as I see it -- getting into Class A airspace wouldn't be terribly challenging for them. Flight speeds would be slow, though -- they are most clearly limited to subsonic speeds, and likely to spend much of their time at relatively slow airspeeds to keep energy expenditure down; they'd also be able to see and hear a jet coming in VFR conditions, but wake turbulence, especially for the combination of a smaller dragon hitting a bigger airplane's wake, would be a hazard to them still, and they'd be large enough to generate significant wake turbulence of their own.