The dumbest irony in the world is the fact that the desert is cold at night. Heat makes people desperate, justifying most cases of insanity. I always imagine people in the desert clamoring over dunes and delirious with heat exhaustion. The cold means clarity. It means precision and sharpness, because energy cannot be wasted in the cold. I’m in the desert at night, three in the morning on a flat, arid plain of Iraq. What I have to do must require some level of insanity, because there is no other justification for it. Yet, my precision is vital. Can’t make a mistake out here, because there is nowhere to hide. I keep flipping the trigger switch over in my hand, staring out at a starry sky, tiny lights poking through holes in a sheet of night. I remember the roof of our apartment

The story here really starts at "I’m in the desert at night..." Everything before that, while well-written, doesn't introduce a story to us. Since it's a nice passage, perhaps you could move it elsewhere and keep it. But where it is now, it just puts off starting the story.

I’m in the desert at night, three in the morning on a flat, arid plain of Iraq.
No complaints here. A good, solid sentence that introduces us to the setting.

What I have to do must require some level of insanity, because there is no other justification for it. Yet, my precision is vital. Can’t make a mistake out here, because there is nowhere to hide.
You are keeping secrets from the reader. It's not interesting unless we know what he's thinking about. Rule of thumb: if the point of view character knows something relevant to the scene, we need to know it too. Otherwise, suspense dies. I don't care how vital his precision is, or that he can't make a mistake, or that there's nowhere to hide. Why? Because I have no context for those thoughts. I don't know why they're important.

I keep flipping the trigger switch over in my hand, staring out at a starry sky, tiny lights poking through holes in a sheet of night.
This feels like stalling. Nothing is happening. Combined with already having no context or understanding of what's going on, you're beginning to lose my interest.

I remember the roof of our apartment building on...
Ok, now we're going to learn something. That's good. But it's too late. We need to learn more earlier.

Also, I caution against starting with a flashback. While it has been done and can work, it tends to kill the forward momentum of the story before the story even gets started.

Overall, the writing is good, but the content is too empty. I need more information about what's going on in order to be interested.