Where the shape comes from
A bird lifting off: the neck and head thrown forward at the top, and beneath them the two wings beating, each drawn with its feathers. The simplified 飞 keeps one wing and three strokes, which is why the character now looks like a single feather rather than a bird. Almost nothing else is filed under it — the radical exists for the word itself, the 飞 of 飞机 and 飞行.