Yep, looks like a fairly common Iraqi vest. (Common for Iraqi body armor, which is still uncommon to find outside of iraq, nice vest!)
Still don't know who made it, but I'm certain it's from the Iraqi supply chain, and not any US Special Forces unit. I bet if somebody could read what I think is stylised Arabic at the top of the label you'd have your answer.
Looks like it's and earlier style, used mostly around 2004-2005, but some can be seen later because of Iraq's poor logistical situation.
Also, it has removable neck guard.
Iraqi National Guard and US soldiers stand on the site where a car bomb exploded in Baghdad Tuesday Dec. 14 2004. A suicide car bomber killed seven people when he struck a checkpoint at Baghdad's Green Zone early Tuesday, the second attack in two days at the district that houses Iraq's interim government and foreign embassies. (AP Photo/Hadi Mizban)
Iraqi women walk past U.S. Army 1st Battalion, 24th Infantry Regiment and Iraqi National Guard soldiers during a joint raid near a mosque in central Mosul, Iraq Saturday, Nov. 27, 2004. The Army took in 29 detainees over 36 hours on Friday and Saturday in Mosul, including eight from this raid. Insurgents rose up this month in Mosul, Iraq's third-largest city, during an offensive by U.S. and Iraqi forces in Fallujah. (AP Photo/Jim MacMillan)
A U.S. Army 1st Battalion, 24th Infantry Regiment soldier leads Iraqi men suspected of insurgent involvement from the scene of a joint raid by Iraqi National Guard and U.S. forces near a mosque in central Mosul, Iraq Saturday, Nov. 27, 2004. The Army took in 29 detainees over 36 hours on Friday and Saturday, including eight from this raid. Insurgents rose up this month in Mosul, Iraq's third-largest city, during an offensive by U.S. and Iraqi forces in Fallujah. (AP Photo/Jim MacMillan)
An Iraqi National Guard soldier looks up at a U.S. aircraft before leaving to remove the bodies of two men found murdered in Mosul, Iraq, Thursday, Nov. 25, 2004. Twenty bodies were found in Mosul in the past week, including ten identified as Iraqi regular army soldiers. Insurgents rose up this month in Mosul, Iraq's third-largest city, during an offensive by U.S. and Iraqi forces in Fallujah. (AP Photo/Jim MacMillan)
An detainee leaves Iraqi National Guard barracks in Ramadi, Iraq, Saturday, Dec. 11 2004. Some 140 detainees were brought to Ramadi from Abu Ghraib prison Saturday and released. (AP Photo/Omar Aboud)
U.S. Army and Iraqi National Guard soldiers remove a body found near a cemetery in Mosul, Iraq, Sunday, Nov. 28, 2004. Ten bodies were recovered Sunday in Mosul, where at least 50 people have been murdered in the past 10 days. Most of the victims are believed to have been supporters of Iraq's interim government or members of its fledgling security forces. (AP Photo/Jim MacMillan)
Iraqi National Guard soldiers remove the bodies of four murdered men found in a cemetery as U.S. Army troops secure the perimeter in Mosul, Iraq, Sunday, Nov. 28, 2004. Ten bodies were recovered Sunday in Mosul, where at least 50 people have been murdered in the past 10 days. Most of the victims are believed to have been supporters of Iraq's interim government or members of its fledgeling security forces. (AP Photo/Jim MacMillan)
Iraqi National Guard soldiers remove a body as U.S. Army troops secure the perimeter after four murdered men were found in a cemetery in Mosul, Iraq, Sunday, Nov. 28, 2004. Ten bodies were recovered Sunday in Mosul, where at least 50 people have been murdered in the past 10 days. Most of the victims are believed to have been supporters of Iraq's interim government or members of its fledgeling security forces.(AP Photo/Jim MacMillan)
Iraqi National Guard soldiers remove a body after two men were found murdered in Mosul, Iraq, Thursday, Nov. 25, 2004. Previously, 20 bodies were found in Mosul in the past week, including ten identified as Iraqi regular army soldiers. Insurgents rose up this month in Mosul, Iraq's third-largest city, during an offensive by U.S. and Iraqi forces in Fallujah. (AP Photo/Jim MacMillan)
I've now got multiple sources saying the soldiers wearing them are members of the national guard.