Well, first bit of wisdom to really understand is that Pecking Order behavior is necessary for chickens. It is The Chicken Way. As painful as it is for us humans to observe it, if we mess with it, it just prolongs the process.
Each and every time you change their location (new coop, move from brooder to coop, etc.) they start it over again. Every time you introduce another bird, it starts over again. That's one reason why it's best to introduce more than one chicken at a time, rather than introducing one, and then another later, and another later, etc. Try to do a couple or more at a time, so the pecking order process isn't keeping your flock all a'flutter for a prolonged period of time.
The method I use is this:
First, quarantine new birds. The recommended time period is 30 days, and this is away from your flock, because some stuff is air-borne.
After that, put the bird(s) into a separate coop, either next to the chicken run or inside it. If you set it up inside the run, use garden stakes and some chicken wire to make a small pen around the "integration/segregation" coop. Give them their own feeder and waterer. Keep them there for two weeks.
During that time, they will see the original flock through the chicken wire, and the original chickens will see the new ones, as well. They'll hear and smell each other, too. And be able to do chest bumps through the chicken wire but NOT injure anybody. There will be interest, and posturing, and maybe even some pecking through the chicken wire, but not enough to injure anybody.
After two weeks, take down the temporary fencing and let them mingle. The new chickens will not be "Strangers" any more, and most of the pecking order business will be conducted around feeders and waterers, so keep the second set up for the new birds for a while.
There will be some squawking, some running, some pecking, but probably nothing more than that. Keep an eye out for any blood-letting; if there is no bloodshed, leave them alone to complete the process, no matter how loud somebody squawks, how much somebody runs and hides, or how much chest-bumping or neck feather flaring goes on. That HAS to occur, whether it bothers US or not.
Do not interfere unless there is blood shed. Feather plucking is normal.