Megan H. answered 03/22/19
Professional, Energetic Writing Teacher with 9 Years of Experience
You're absolutely right that a flag cannot fly people; even in a poetic sense it means nothing.
I think the original quote you read is simply missing a word (perhaps a typo by its original author). I think it was intended to be "At the empire's height, her flag flew OVER more than five hundred million souls and over a quarter of the world." This guess is supported by the fact that a second prepositional phrase which also starts with 'over.'