Yes, the adults can peck the chicks quite hard, probably even kill them. There is no love between them. I think you are doing quite well with your set-up. I can describe our set up if it helps. We have raised about 6 batches of ducklings and chicks from incubator to adults very peacefully.
We hatch eggs in the incubator and they live inside in a big tupperware bin (we live in a pretty cold climate, plus I love having chicks in the house, LOL) and slowly introduce the chicks to the flock for a couple hours at a time (like we will set the chicks outside on warm weekend days or afternoons when we are there to keep an eye on things) but always in a situation where the chicks can escape to an area they cannot be pecked to death. We have kennel panels meant for dogs set around their brooder and feed and the chicks can fit between the wires, but the large chickens cannot. The chicks do not have good self-awareness however and can easily get "lost" and wander outside the kennel and not know where their pen is. They will peep loudly because in nature, the hen would hear that and (presumably) come and rescue the chick. With our set up, that task is up to us humans so we only set the chicks out if we are going to be around to intervene.
We also give the adults treats (they love cheese and dried grubs) in their first several viewings and interactions with the chicks. With horses, I've heard people talk about trying to making sure there are good experiences associated with introducing something new. Then the animal associates the new with good. We want their first experiences with the chicks the be positive. We have two bantams who really don't like chicks when they are broody and this helps their attitude.
It also helps if the adults have room to roam. Ours roam over about 1/2-1 acre and if they have that much space, a lot of times they couldn't care less about chicks. They mostly leave them alone (other than trying to eat the starter/grower feed - our adult hens love starter/grower feed).
After a few months the chicks have always integrated very peacefully in our experience. There is no major turning point. It just happens naturally that as the chicks age they start hanging around the periphery of the flock, and then integrate. There is nothing more peaceful than watching the integrated flock out pecking in one of our pastures. I love chickens! Everyone just needs lots of time to see each other under low pressure, happy situations, and then they get along.