I did a lot of research on this a few years back and ended up with the exact jacket. It's a Korean War era M-1951 Field jacket with the drawstring at the waist and buttons and zipper on the inside. They're on ebay pretty regularly but run big so size down.
Want some other Quint gear?
Buy a yellow JAWS t-shirt.
Yes, I **** you not, this is Robert Shaw wearing a Jaws t-shirt. No photoshop, straight up:
How awesome is that?