This question has been answered at the following link:
The kites have many different symbol meanings throughout the novel, e.g
When Amir takes part in the tournament the kites represent:
Amirs needing for Baba's attention, The conflict in Afghanistan and even the will to survive connected by a piece of glass riddled string or to be free cut from the string experiancing freedom.
And as other people have mentioned the kite eventually represents betrayal as Amir left Hassan, further reinforcing my earlier point of the kites representing the conflict in Afghanistan, when Amir returns to his hometown he finds out that kite flying is banned showing the Taliban could be symbolizing "there is no conflict, we own this land anyone who opposes us will be dealt with etc".
The blue kite is a symbol of Hassan's loyalty to Amir. Hassan will not let go of the kite or his loyalty even when he is in danger of being attacked by Assef. Hassan remains loyal even after being betrayed and framed by Amir.
How about in the first chapter...floating like eyes looking down at me...?
He was never able to run from his past?
The kite symbolizes a few things. It symbolizes freedom, that which flies freely in a country which doesn't allow this. (Soon after). It symbolizes hope and a happier time in history (and youth). It symbolizes the culture of Afghanistan and how all the people unite to this one event. And it becomes a equalizer of class, religion, background and otherwise atheltic ability to which the author had little.
-the main symbol of the blue kite in the kite runner is the symbol to Baba's attention. Amir thought that he would only earn Baba's love and attention if he won the kite running competition. Also, he wanted to show all the kids when he got back to school that he won and he cut down the runner-up kite.
-But as the novel continues, the kite becomes the symbol of bretraying. Hassan sacrificed himself to bring the kite back to Amir. Hassan was very loyal to Amir. Amir then betrayes him.
-At the very end scene of the novel, it is Amir running a kite with Sohrab(Hassan's son), who he now is raising, and it shows happiness, and peace at last.