I just keep throwing eggs back towards the fire, (I have 2 fires going) then move 2 chickens away from the large gathering of chickens that I have sectioned off. I spam build signs to seperate them & guide them away from a mating pair. This keeps the eggs coming, and also groups more chickens together for mass culling & collecting.

For the breeding pair I typically go about at least 3 corewood logs (4M) long away from the main group, so they are not disturbed by population per/ area issue. Still testing it somewhat however. I've tamed heaps of boars before so assume this is similar in fashion to that a bit.

Anyway might be a bit of trial & error try a few things out, see what works & what won't.