While one could logically argue that Baba, Amir, and the country itself are all protagonists, Amir meets the requirements most thoroughly of a tragic hero.
Tragic downfall: Amir is viewed as the only son of one of Afghanistan's most prestigious businessmen. He not only literally falls from his wealthy, respected state to being an unrecognized struggling immigrant in America, but he also figuratively falls out of favor with "God" or morality because of his betrayal of Hassan.
Tragic flaw: Amir's tragic flaw is jealousy/selfishness. He wants Baba's approval so badly that he is willing to get rid of or sacrifice anything that gets in his way. While he sacrifices Hassan in order to get the last fallen kite, he also realizes that if he gets rid of Hassan, he will no longer have to divert Baba's attention from the young servant boy.
Tragic realization: When Amir realizes that he must go back to Kabul to rescue Hassan's son and ultimately faces Assef again, he experiences somewhat of a realization that he has brought most of his trouble upon himself. His true realization occurs when he recognizes his responsibility to Sohrab and pursues adopting him and bringing him to a safe place--America.
While Baba also goes through the main steps of a tragic hero, he dies before he truly has an opportunity for a tragic realization. He never confesses to Amir that Hassan is his half-brother or truly apologizes to Amir for showing no interest in his writing until he is on his deathbed.
Likewise, the jury is still out on Afghanistan. Perhaps it will have a happier ending and a positive "realization." Right now, the situation is very grim for Hosseini's homeland.