Kite flying symbolizes competition as Amir was constantly competing with Hassan for Baba's affection (as he was jealous of the amount of affection Baba gave Hassan), just like how they're competing with other players to win the competition. Moreover, Amir simply wanted to win the kite flying competition to make his father happy, and proud.
In terms of how kite flying also symbolizes sacrifice, and guilt, kite flying symbolizes sacrifice and guilt as Hassan sacrificed himself to obtain the blue kite for Amir, while Amir ran after watching Hassan get raped, assaulted, and used as a sacrifice. This is illustrated in the