Legendary pokemon Tornadus from Black/White is the first and only pure Flying type.
All other Flying types have Flying as the secondary type, most commonly with Normal. The exact reason it was like that is unknown. In most games, the first routes are nearly all Normal type, so this is probably why pokemon like Pidgey have the Normal type.
Then they just carried on that trend with Spearow, Starly and so on. So any pokemon based on birds are Normal/Flying unless there is a call for a different type like Water/Flying. Tornadus is based on a tornado, not a bird, so is pure Flying.