Honestly, I think the concerns over complexity or time are overblown, so I put together a really quick video on the dogfight phase, and essentially played out two dogfights, with explanation, in just under eight minutes.
Now, while the phase itself I think is pretty simple and straightforward, I didn't touch on one of the other big concerns, which is whether it's fun, particularly with the risk of having a flyer never actually reach the board, which could have been the case with the Night Scythe in my first example. Honestly, to me, this is a bigger concern.
As I mention in the video, while the instructions say to put the models on the board, the models are largely irrelevant and it is a simple exercise to simply talk out the distance and positioning of the models.
Despite me glossing over the fact that you measure from the weapons to hull for flyers, the point remains that generally you can simply talk out the range bands you'll be using for the dogfight and stick with them.
One issue I see is that the shooting and line of sight is implied to be abstract in the rules, as it talks about flyers who are facing away from their opponent only being able to fire snap shots. There could be an argument made for most flyers not having arc of fire at all as positioned, but I believe the attempt is to use the weapons abstractly. As a result, a simple agreement that the stated range is the range to/from all weapons on both sides is a simple solution and errata that could be made.
Anyway, in summary, the dogfight phase doesn't have to be long and complex, but offers a bit more risk/reward to the equation when bringing flyers, and I generally like the Death from the Skies supplement, Dogfight phase included.