From what I can understand, most of the Iraqi Airways fleet was scattered around the Middle East prior to the liberation of Kuwait.
The fleet is pretty old, with a selection of 727's and 747's which haven't moved for over ten years.
It's rumoured that the Iraqis still have a 747, a 727 and a couple of old Russian transports remaining in Iraq.
The Iraqis stole four aircraft from Kuwait Airways after the occupation, two 767's and two Airbuses which were subsequently destroyed on the ground in Iraq by Allied forces.
But to answer your question, with the exception of the odd Hajj flight sneaked past the UN, there haven't been any scheduled Baghdad flights for years.