There's not much to say about the writing style: it's bare, stripped down, and more or less recedes into the background. Hosseini is much more interested in plot development and irony than in dazzling us with The Prose To End All Prose. And that's OK: his plot has the resonance of tragedy. Too present a writing style might distract from the plot.
That said, we do want to point out a stylistic quirk in The Kite Runner. The descriptions often mimic the camera movements and cuts of movies. In an interview, Hosseini admits the book uses the language of movies but denies he intended to do so (source). Suffice to say, it's there. In addition, there are tons of references to American movies and movie stars. Just a coincidence? We think not. Here's an excerpt from the book – picked at random – to prove our point:
I caught a flurry of movement out of the corner of my eye. The a blur of something zipping across the room, and the next thing I saw was Karim slammed against the wall, his sandaled feet dangling two feet above the floor. Wrapped around his neck were Baba's hands. (10.40)
To us, that sounds like an action movie. Descriptions like this one are everywhere in the book. Hosseini, whether consciously or not, is mimicking the quick cuts of the contemporary film action sequence. In addition to all the movie stuff, Western goods pervade the book's pre-Soviet and pre-Taliban Kabul. (Jeans, Ford cars, Schwinn bicycles, etc.) So what does this all mean? Well, the novel has the simplicity necessary to tragedy; but it also has the occasional dramatization of Hollywood. Hosseini's combination of the two makes for a rollicking good read.