Sorry, but I had one issued to me when I deployed to the gulf in 2003. I was in a rear area unit then, and when I deployed again in 2005 we all got the kevlar, but some were issued the flak jackets at the start of the war.
Which branch? I tend to follow the Marines more closely than other branches of the service, and was told by a friend that the Vietnam era flak vests were long gone from Marine inventory; I assumed that since the Marines are always the last to get new gear and the last to get rid of the old that this was the case for all branches.