A flak jacket was a protective piece of clothing used by CTU agents to reduce damage caused by gunshot wounds.
Jack Bauer had a flak jacket in the cabinet in his office, which he placed on Nina Myers after holding her at gunpoint. On orders from Ira Gaines, he drove Nina to an oil field and shot her, but he deliberately shot the armour within the jacket, so Nina was merely bruised by the gunshots. Through video footage, Gaines was convinced Nina was killed, but she survived to inform CTU of Jack's actions. ("Day 1: 6:00am-7:00am")