If you have a rooster then an all flock or flock raiser with oyster shell on the side is best in my opinion. The rooster doesn't need the calcium, it's not good for chicks and the hens will have the oyster shell as needed.
Lots of greens, they like fruits and vegetables too. Bugs of various sorts. Mealworms, black soldier flies and crickets are popular here. The local lizard population starts a frenzy.
I don't see any reason not to give scratch. It doesn't have to be corn or soy based and chickens enjoy foraging and pecking at the ground when they eat. They like seeds as all birds do. I give my flock Bar Ale 6 way scratch and pick up pigeon feed without corn in it from a local feed store.
When your chickens molt they'll do well with added protein which they need to regrow feathers. My flock likes fresh or canned salmon, cooked hamburger and poached poultry.