I always integrate my chick at around 6-8 weeks. Younger birds are a natural addition to a flock. Older birds are intruders.
I always start by penning the young group where everyone can see them but they can't touch them. After about a week the older birds are used to the chicks and I begin letting them mingle. My pens are in my chicken shed, so it's just a matter of opening the door and than watching and if necessary playing referee.
The chicks are usually ignored with an occasional peck from the older birds. After a bit I round them back up and do it again the next day. After about a week I usually leave the chicks out all day. I continue to lock them separately for another month or two until I feel comfortable leaving them out.
The bigger your set up, the easier it will go. Crowding birds makes it harder and will take much longer. Integration is all about patience and making decisions based on behaviors you observe.
X2. And if they can free range together during the day, that seems to make integration go faster. For a while they might want their own sleeping quarters but after a while a few might move across, especially if you give treats in the coop you want them to go in at night or once they are sharing feeders and free ranging for a while I sometimes just pick the resistant ones out of their coop some night after it is dark and put them where I want them and at that oint no one seems to mind.