Here's how it works in Chicken World when new chicks enter the world of big chickens. They observe and learn. It is, after all, incumbent upon them to learn how to fit into the hierarchy of a flock. So, first step is to watch and learn.
I raise my new chicks from day one, usually they are one day old, in my enclosed run. They have their own chick brooding pen, safe from the older chickens, but they are completely exposed to the flock. This serves the purpose of letting the older ones become used to the small ones being members of the flock, therefore they belong and are not outsiders.
The more important lessons being learned, however, are ones the babies are learning about the adults. At day two or three of these lessons, baby chicks are still more instintively drawn to any warm, fluffy, chicken underside, and can't be trusted not to get into tragic trouble by trying to scoot under the wrong butt.
The chicks are discovering which chickens seem to be more fired up and dangerous and which are mellow and pose little risk. By the end of week two of observing the adults and having become a bit more savvy about safety, they can then begin to mingle with the adults.
With your older chicks, I suggest you do something similar. Set up a play pen for your chicks in the midst of where the adults spend most of the day. If you aren't set up to house the chicks in the coop at night in a safe enclosure, it's fine to let this "meet'n greet" take place just during daytime.
For older chicks, it takes about a week for the chicks to size up the adults. Now we talk about how you make it safe for the new ones during this phase of integration. You provide a "panic room". This is any setup where the safe haven has two or more chick entrances that are too small for the adults.
The chicks' food and water is inside this haven, and it will insure that the chicks get all the food and water they need without the bigger chickens eating it up before they get their share. This should continue with an alternative feeding station until the youngsters are fully grown and can compete for food and get what they need. I have five-month olds that still haven't grown enough confidence in muscling their way to the feeders, and I have to find a way each day to slip extra food to them so they don't fall behind in development.
This is already too long. So, if you have any questions, feel free. Others will be along soon to chime in with other good ideas.