The Iraqi Air Force is not very effective. It not for lack of trying. The government has spent billions to buy new aircraft, support equipment and weapons (including Hellfire missiles). Money isn’t the problem, people are. During decades of rule by the Sunni minority (the last Sunni leader being the late Saddam Hussein) the Sunnis monopolized most technical jobs. That included flying aircraft and maintaining them. With the overthrow of Saddam most of those Sunnis fled the country and many of those who stayed were not trusted by the Shia majority (who now controlled the government.) The Shia now had plenty of access to all those good tech and management jobs the Sunnis had long monopolized. The problem was that not enough Shia had the skills or experience to handle all the high tech work now available. The military was worst hit by this shortage because commercial firms could pay the market price (high) for the few competent Shia technical specialists. Moreover, government corruption is more of a problem for those working in the military and there is more dangerous (especially for aircraft crews).
This is not a solution unique to Iraq, it is common in all the Arab Gulf oil states. The situation is worse in Iraq because of the Shia/Sunni issue and Iraqi refusal to hire a lot of foreign (often Western) specialists to maintain the aircraft and other technical jobs required to keep an air force operational. The other Arab oil states have no problem hiring a lot of foreigners to do the tech jobs. But in practice the Iraqis do hire a lot of Westerners for these jobs. The difference is that these men are hired officially to teach Shia how to do the work. Since this can take years, and the government does not want to send up aircraft that will likely crash because of poor maintenance, the Western “instructors” often do a lot of the work or carefully inspect what is done by their Iraqi apprentices and fix what needs fixing before clearing the aircraft for takeoff.
But with nearly all military pilots being Iraqi there are limits to what these fellows can do. Many are newly trained and some of the older ones are Sunni who tend to be watched closely. There are never enough pilots and because of the skills and experience shortage there are limits to what they can do in the air. For example, only three aircraft are equipped to fire Hellfire missiles because there are few pilots skilled enough to handle this.
The situation is improving very slowly, in part because the government wants F-16s available for service. To that end 36 F-16s have been ordered and even more Iraqi pilots selected to train to handle these more complex aircraft. The F-16s won’t be in service for about five years but in the meanwhile the air force has a collection of prop-driven single and twin engine aircraft and some helicopters to support the troops. Iraqi soldiers really miss the American air support.