All things to do with flying are integral to this book. A lot of our discussion about flying can be found in "Characterization" and "What's Up with the Title?", so be sure to check those out. But what we will say here is that wings, the stars and moon, airplanes, dragons, and kites are all within the realm of "Flying and Sky Imagery."
The theme of flying in Dragonwings is connected to everything, because the story is itself dependent on what flying stands for: believing in a dream and pursuing it. Uncle Bright Star might think Windrider's dream of flying is bunk, but that's because airplanes hadn't been invented yet. You can fly from Beijing to San Francisco now if you've got the money and documents, but a hundred years ago, that was hardly imagined to be a reality by most people. Since Windrider believes his true identity is as a dragon, to believe in his dream of flying is the same thing as believing in himself.
Moon Shadow understands that it is important for him to believe in his dad and to support him, even when other people push him away as a crazy. That's probably because one of Moon Shadow's dreams was to meet his father; once he meets him, he's going to do all he can to hold onto that dream of having his father as part of his life. And in order to show how much he cares about Father, Moon Shadow supports his dream of flight and does everything he can to make it happen.