Unlike the US who issued restrictions (below). There are likely Iranians and others wanting to high-tail it out of Iraq.
FAA Statement:...Jan 7, 2020
NOTAMs issued outlining flight restrictions that prohibit U.S. civil aviation operators from operating in the airspace over Iraq, Iran, and the waters of the Persian Gulf and the Gulf of Oman.
Kurdistan Government official stated that no American military base or consulate was attacked in ‘Erbil city’, Kurdistan Region.