The most gentle way to introduce a few new hens to the flock?

Introduce the birds to each other by using a Berlin Wall of deer netting between the two groups. After a few days of getting to see and hear each other, without touching each other, they'll calm a bit. After a few days, blend flock while outside in the run, in the late afternoon.

Mixing up the old flock also works well. Take the two top hens out of the established flock and put them in separate pen for 7-10 days, mix the remaining members with the new birds. Outside in the run is best. After the 7-10 days, re-introduce the old leaders.

Moral of the story is to break up the old pecking order. This shakes up the old flock enabling the newer members to integrate more easily, as everyone is looking to find their place.

 

You should have a temporary coop or crate for new birds. Letting them see one another throughout the day and definitely free ranging together gets them to introduce themselves slowly. Pecking order is their nature so to slow down the process is advised. Injuries will happen if you simply lock them up all together. There is plenty of places to get away from dominant hen when free ranging. If they can't get away then they'll get injured, the aggressor will think the weaker hen still wants to challenge authority.

Slow introduction and the new hens usually tell me when they are ready to be apart of flock by going into the big coop at night on their own. I still allow a large area for them during day together for another week after newbies go to coop on own.

 

Okay, this is some info supposedly told by a really ancient chicken woman. Im not sure where I read it.

Keep your new birds, group A, separate from your current flock, group B. Feed them for a few evenings right at roosting time.

Then after three days of this, put group B to roost in the evening without any feed. Give them only water starting about 4 hours before sundown. Also deny group A the same feeding.
Once group B has settled on the roost, quietly bring group A into the coop. Use no lights except a red flashlight.
Place the newcomers in among group B on the roosts and sneak back out.

In the early AM, just as the birds are rousing, enter the coop with a clattering and clanging feed bucket. Make a lot of racket as you pour the feed to the birds. In the ensuing commotion the birds will get busy feeding and forget the usual henpecking given to new birds. Once the feeding is over, let them out as usual.

This supposedly takes advantage of the bonding influence felt during feeding. There will probably be some squabbling, but it should die down in a day or two.

If this doesn't work, then just let Nature take it's course. They're chickens, after all.