Barn paint is ideal for the exterior because it’s designed to be applied over unprimed, rough-surface wood and to hold up to farm outbuilding conditions. The interior doesn’t need to be painted or sealed. It’s better to allow the wood to breathe.
A chicken coop will not need to be wet-cleaned except in extreme, unusual conditions. Keep it dry, keep good bedding on the floor, and keep it well-ventilated and you can dust out any cobwebs, etc. when you change the bedding if you want to. n