How thick is a flak jacket?

Al Franken is in big trouble for groping a woman who was sleeping.
It was designed to embarrass the woman, and was absolutely wrong.
However, she was wearing a flak jacket.
I am wondering how thick the flak jacket is, and if it would defeat the tactile thrill of feeling her up.
Once again, what he did was awful and wrong, but there is a difference between copping a feel on a sleeping woman, and posing for a joke picture without actually being able to enjoy the touch.
Again, what he did was shameful.