They do not sunburn. The exposed skin does either turn very red(roosters) or combination of red/darker pink(most hens). This color change is actually a sign of healthy and thriving bird. Also cockerels/pullets usually are light skinned until they are 'mature' then the skin gets darker- another thing against the sunburn claim and seems more like possibly a chemical or ??? response to direct sunlight. Same response shows up on most chickens if any part of their skin becomes exposed.
There's a website that says they sunburn but I say nonsense. Tried to let 'em know but it's still up there.