This is also something I looked for a while ago and couldn't find anything really definitive. As noted by TheOttoman above, The Gulf War Air Power Survey (GWAPS) vol. 5 has a table of the overall aircraft roles (e.g. fighters, bombers, etc.) and numbers, but it doesn't break it down any more. In my earlier searching though I found this page on globalsecurity.org that does list the specific airplane types and numbers, though it doesn't have any details on their serviceability or bases. (Tangentially related, see this globalsecurity.org page for information about Iraqi air defenses and SAM sites.)
I also found this ACIG Journal page detailing Iraq's invasion of Kuwait in 1990, which may have a bit more information. The page was offline for a while but now may be back up, behind a registration wall, here and there may be other articles there worth checking out.
Finally, I did another set of searches just now and found a source I hadn't seen before, regarding something called the Gulf War Toolbook (PDF). The PDF linked here is to a 34-page user's guide which seems to be for some kind of interactive software, but I haven't been able to find anything more on it. However, the user's guide cites some sources, in particular, "The Gulf War Fact Book" and "The Gulf War Order of Battle", the latter of which it unfortunately says is unpublished, but lists Larry Bond (of Harpoon and technothriller fame) as an author.
I found The Gulf War Fact Book on Amazon and ordered a copy; when I get it I'll post again with any information I find in it.