** Click on Title to see full answer ** Interestingly, the military itself has looked at this issue at least a little. In DTIC (Defense Technical Information Center), the search: "carbon footprint" gets 27 reports, on such issues as energy efficiency, public concerns about the military's use of energy, military and other government use of already existing commercial transportation, etc. Even the specific search: "carbon footprint" and iraq gets 4 hits. These appear to be mainly from the full text of fairly popular service members' magazines and newsletters. DTIC is free to all, and even though many reports are NOT full text, it would be worth skimming through other searches such as "energy efficiency" and calculation and iraq (101 hits) to see if there are more technical and detailed reports.
The Department of Energy's OSTI site is a quicker path to full text technical studies, but may not have much on the Iraq war. To shortcut to full text, Look in the Left side column under "Key Resources" and point the mouse to "Science Accelerator" but DON'T click it - go to the menu that opens and click "Information Bridge" which is ONLY full text reports. Or go to the right side of the page and click the "Key Databases" link to find Information Bridge.
I find that the basic (default) search of these pdf full text reports can be quite tricky. "Carbon footprint" and iraq gets 2 hits, but then you might have to plow through a LOT of pdf text to see how you got the result. I have had very mixed success with pdf searches, and don't trust them to find all instances of words. Advanced search can save time, by letting you search subjects or titles. But it's a trade-off; the full text search can find one or 2 very good paragraphs in a 300 page report, even if the whole document is under a vastly different subject. The very broad subject: iraq gets only 22 hits as a subject search, and they don't look too promising at first glance. I would be tempted to first skim through the 68 hits in full text for: "iraq war".
Commercial databases don't look too hopeful. ScienceDirect (it is searchable full text of highly technical journals - available onsite in large academic libraries only) gets 3 hits in full text for: "carbon footprint" and iraq, and these don't appear to be directly related to the war. Even the fulltext search: "carbon footprint" and war gets only 11 articles; "carbon footprint" and military gets 9.
The more multidisciplinary, partially fulltext database Academic Search Premier gets 53 hits for TX (all text): carbon footprint and iraq, and they look highly doubtful - probably the war is mentioned only in passing, maybe many pages apart from carbon footprint. If you have some time to skim through, also try co2 footprint and iraq (2 hits in Academic Search Premier).
You can also try multiple sources at once in services such as science.gov and usa.gov. Usa.gov gets 23 hits for: "carbon footprint" and "iraq war", but I suspect many are simply congressional testimony or hearings that cover both issues separately. Science.gov searches 31 files at once. But for the search: "carbon footprint" and "iraq war", it ends up getting 2 of the same hits I got in the www.osti.gov "Information Bridge" search mentioned above.
I will try to dig around a bit more for this, but there may well be no full answer to it anytime soon, because much of the information on fuel use in the war is classified. Even if we could get reliable estimates of Army, Navy, Air force, Marines - or even combined DOD appropriations for fuel, there still is the question of supposedly "private" operations, or CIA, etc. secret projects.
But it is certainly worth trying to compile whatever IS published. Even the official reports could be very useful, if you have the time to plow through them and calculate likely totals and averages.