I think that Hosseini's work displays the theme of power in a couple of ways. One specific way would be through Assef. In this rendering, power is shown to be predicated upon authority and control. As a youngster, Assef is able to display power in the social stratification that places he and Amir above someone like Hassan. It is this display that compels him to rape Hassan. If nothing else, the rape is representative of how Assef has power and how Hassan lacks it. This helps to bring out how Hosseini defines power in modern day Afghanistan: Someone has power at the expense of someone else. Assef carries himself in this manner as a member of the Taliban, another construction of power that is more zero sum than anything else. The Taliban are shown to hold power over others because they possess it and others do not. The exclusivity of power is what enables them to establish and consolidate their control over others. In this, power is shown to be something that excludes other and in this exclusion lies a dramatic decrease in power. When Hassan leads the stoning of the couple in public or the imprisonment of Sohrab, it is a reminder of how power can be designed to limit worlds at the cost of others' expansion.
Power is expressed in many ways in The Kite Runner. One way to think about it is the personal power of individuals, as expressed in the power to make choices. The ability to choose -- a privilege that Amir (as a Pashtun and Sunni) has, but Hassan (as a Hazara and Shia) does not -- is one way this "personal power" can be understood. An example of this is Amir's reaction to Assef's rape of Hassan. In a way, Amir's decision not to fight to protect Hassan is an expression of personal power -- his privilege allows him to betray his friend. In the same way, Amir's privilege allows him to immigrate to the United States, while Hassan ultimately ends up in an orphanage.
The rise of the Taliban, and Assef's becoming a Talib, provides another way of thinking about personal power at the end of the book. Amir, driven by guilt over his earlier betray of Hassan, now uses his privilege to seek out Hassan's orphaned son, Sohrab; the political reality of Afghanistan is reduced to his personal confrontation with Assef. While his fight with Assef for Sohrab is a kind of literal contest of personal powers, it's not clear that Amir's eventual victory, or the set of choices that led him to fight, will atone for his earlier betrayal. For good or bad, Amir will always be formed by the choices he was privileged to make.