People who raise goats or sheep sometimes use a "creep feeder" that lets the babies in to eat extra food, but keeps the adults out. Something similar might work in your case, letting chickens in but keeping goats out (this depends on the goats being a certain amount bigger than the chickens. If you have giant chickens and tiny goats, it might not be possible.)
Chickens do need to be able to eat during most of the day.
For most people and most chickens, it works better to keep chicken food available all day long.
@U_Stormcrow has chickens free ranging in a large area, with many things available for them to eat. So those chickens have something to eat all day, even when it is not purchased food. He also butchers chickens regularly, and checks how much fat they have, and provides more or less of the purchased food according to what he sees. (It is really hard to tell how much fat is on a live chicken, but pretty easy when you are butchering the chicken.)