"My tan is peeling" refers to when you have been out in the sun a lot, and your skin begins to become flaky and peel off in some places (usually the shoulders). "He was lost in action in Vietnam" means the man fought in the Vietnam War, and he didn't come home. Being lost in action means they don't know if the soldier died or not, but they generally assume they were one of the dead who were not identified. It is also possible that they were a prisoner of war, or that they abandoned their post. The official military term is "missing in action" and it is often simply referred to as MIA.