I tried to search for LHR
-Baghdad flights on BA
.com, and got this message:
"British Airways does not currently fly to Baghdad"
Security in the area is still not stable enough to justify the risk of commercial flights. Plus, the limited commerce in the area doesn't justify the expense. Airborne and other cargo carriers have flown supplies in, and some commercial airlines may have run charters, but that's it.
I would think that BA
, KLM, Royal Jordanian, and Emirates would be among the first airlines to fly to Baghdad. The oil industry will support most of the original flights.