Please understand I in no way consider myself an expert in this.
However, in the last two years, I have integrated dozens of birds.
The fact you have a roo will help. He is the king. Hopefully he will
help the pecking order establish itself quickly.
The more room you give the birds the better off you are. If you have
a small coop and throw in new birds there will be fights. If you have
a run area or the ability to integrate them while free ranging that will
help a lot.
I've tried the "put them side by side" technique where they are
supposed to get used to seeing each other. It didn't work for me.
The best results I've had is when I merged 2 existing flocks, one
older and one young together, especially when there is a roo present.
Expect it to be nasty at first. Those Red Stars may get aggressive.
Some of the young birds may adjust fine and others may just go nuts.
A bird running around frantically is an attractive target for the older hens.
I've had to cull a few birds who were just causing way too much
commotion in my main flock.
Finally, patience is key. It looks a lot worse than it usually is. They will
take weeks to fully adjust to one another.(possibly)
My last integration was sorta easy. I threw a bunch of 10 week old fryer
roos, some accidental fryer hens, and two turkies in with my layers. It
went well.