In The Kite Runner by Khaled Hosseini, there are moments when Amir is selfish; however, his character overall is not entirely selfish. When Amir is young, he vies for the attention of his Baba, yet his Baba is critical of him and always pushes him to perform better. Amir is jealous of the attention that Baba gives to Hassan because he does not understand why Baba would need to show Hassan such affection. So, one might argue that in the earlier parts of the story, Amir is selfish because he wants this affection for himself. (Although I think Amir is more conflicted at this point than he is selfish.)
However, the majority of the novel concerns itself with developing the road to redemption upon which Amir embarks to make amends for his ill decision in the alley way. Amir does want to set things right for himself, but he also wants good for others such as Hassan's son. So overall, Amir is not a selfish character.