I think that might be difficult, since you have to be ordained within your denomination in order to be considered to be a chaplain. I don't know if the Freedom From Religion Foundation has got to the point where they ordain atheists: it might be profoundly against the point.
Although the Flying Spaghetti Monster crowd would probably start ordaining people if there was enough interest in it within the military.
I think being a chaplain in the military is a very challenging job — meeting the requirements of the denomination as well as the requirements of the military, while preaching a prophetic call could sometimes be at odds with each other.
But as there are more and more atheists in the ranks, it will be something the military should consider.
