When a friend and I accepted this quest (we were in a party together), I was an Obsidian Nightwing and he was mounted up on me. That resulted in me getting the free flight with Khadgar to Azsuna, and my friend being dismounted and left on the Krasus Landing without a free flight.
So he had no way to get to Azsuna since he hadn't been there yet, thus not having any flight paths there. I started searching on the web to see if anyone has had the same problem in the past and solved the problem. The only thing I found was that Khadgar had been missing when landing, and also that if you abandon the quest you will not get the XP from the quest since you can't pick it up again (maybe in his case Khadgar would have showed up on Krasus Landing again, but he didn't want to take the risk). So the only thing left was to try and find a way straight from Dalaran to Azsuna....
Ok, so Dalaran is high up in the air, and Azsuna is on land far down from there... So you can't exactly swim there.
But what you actually can do, is to find a place in Dalaran near the edge of the floating cliff that Dalaran is resting on, facing Azsuna, and then just jump out and use Goblin Glider Kit, or if you're a priest just use [spell=50195], or if mage just use [spell=12438] or really any other spell/item that you have that will help you get down undamaged. I can't actually confirm that the mage spell works, since he used Goblin Glider Kit that lasts for 2 minutes. Sadly he does not remember for how long he was falling, but I'm not sure 10 seconds is enough. Although maybe you would just land in the water unharmed and could swim the rest of the way, I don't know...
I think he was falling for at least 1 minute. At the end he circulated down in a half circle and landed just on top of Khadgar and was able to complete the quest! It was pretty amazing to see actually!