«وَأَغْرَاهُ عَدَمُ الْعِرَاقِ بِتَطْلِيقِ الْعِرَاقِ»
Lack of even meagre food drove him to leave Iraq behind.
The first ʿirāq is the plural of ʿarq, bones from which most meat has been stripped. The second ʿIrāq names the land of Iraq. The identical sounds link the lack of even scraps of food to the need to leave that land.
Taṭlīq, literally associated with releasing or separating, makes departure sound emphatic. Here it is figurative, not an actual marital divorce.