It's really not necessary. The chickens won't care if you paint it or not. I did because I wanted to and because I think it is easier to clean poo off paint. It won't clean off wood, it soaks in. Inside their coop and nest boxes, I used latex eggshell or satin type indoor wall paints left over from my last home paint projects. Painted their roosts with outdoor stain to match outside of coop.
Didn't really pick out new paint for them, but funny that the Cresant paint I used on the walls nearly matches poop spots so it looks cleaner.