If the story The Kite Runner continued on after the ending, what do you think the lives of Amir and Sohrab would be like?

A followup to a story should be consistent with what went before, I think, don't you? You will have your own ideas as to what happens to the characters, but that is the principle you need to keep in mind as you write your own epilogue. 

As the story ends, we have Amir, who has redeemed himself by rescuing Sohrab, Soraya, who is unable to have children, and Sohrab, of course, who is clearly going to stay with the couple.  Amir and Soraya have begun to involve themselves in the troubles of Afghanistan, for example, by helping to set up a hospital there. Sohrab has been largely mute since Amir has brought him to America, but in the very last part of the book, there is a spark of hope, as Amir is able to engage him in kite running and manages to elicit a small smile from him. 

If I were in charge of planning the lives of these people from this point on, I would have Amir and Soraya adopt Sohrab and adopt at least a few other orphans from Afghanistan.  I would arrange for therapy for Sohrab and be sure that his new parents help him maintain close ties with the language and culture of Afghanistan, which they can do easily with the large Afghan community nearby, particularly Soray's parents, now that they have been told firmly that Sohrab is part of the family. Amir will continue to write and publish successful novels, assuring the family financial stability, and Soraya, once the children are older and Sohrab is more stable, will teach.  During the summers, they will go to Afghanistan and do what they can to help in the war-torn country.  Amir will use his hard-fought wisdom to be a kinder and better human being, able to a credit to his family and his two countries, Afghanistan and the United States. After all that these characters have gone through, we can only wish the very best for them!