The Kite Runner does start with a flashback. It might be helpful to start with the words of the novel.
I became what I am today at the age of twelve, on a frigid overcast day in the winter of 1975. I remember the precise moment, crouching behind a crumbling mud wall, peeking into the alley near the frozen creek. That was a long time ago, but it's wrong what they say about the past, I've learned, about how you can bury it. Because the past claws its way out. Looking back now, I realize I have been peeking into that deserted alley for the last twenty-six years.
Based on these words, it becomes clearer why the novel starts with a flashback. First, as the narrator, Amir, says, the past has a profound effect on the present and future. No matter what Amir does, how old he is, or what he has accomplished, what happened when he was twelve years old has a grip on his life. In other words, the events that took place in that alley in 1975 have shaped him. Amir’s guilt in not protecting and standing up for Hasan, his loyal and best friend, is always with him.
Second, by starting with a flashback, Amir is able to unpack who he is now. More importantly, the flashback shows Amir’s “original sin” and his need for atonement. As the novel progresses, Amir finally gains the courage to go back to Afghanistan and make “atonement” and find redemption. Without heavily emphasizing the past, the novel would not make sense. Furthermore, one of the best ways to depict Amir's need for redemption is to use a flashback.