If you are going to be getting chicks every year or two, as I have over the nine years I've had chickens, you just may join the club and do away with layer feed and just feed grower all the time with oyster shell on the side. When I switched over for good, I discovered my hens far preferred the grower over layer. It's certainly not affected egg production adversely in the least.
With that issue out of the way, integrating chicks with adults is very simple and easy if you use the panic room method. It involves setting up a safe area that the chicks access through 5 x 7 inch portals, and their food and water is kept inside this refuge. That way, there's never any danger that the older chickens will chase and bully the chicks away from their food and run the risk of them becoming malnourished. I integrate my chicks at three weeks using this method and it's safe and reliable. I advocate brooding chicks alongside adult chickens to make integration even easier.
The 5 x 7 inch portals accommodate the chicks until they reach three months, and by that time, they're more than holding their own against the adults and no longer need a refuge.
You can read about it and see pics by clicking on the second link below my post, the article on brooding outdoors.