When should I be breeding for replacements?
What are your goals? What do you expect to get out of your chickens? I'll assume it's for eggs and that you want some eggs in winter but if you are breeding for show or some other reason my answer might change. More out of curiosity than anything else, what breeds do you have?
Each individual chicken can be different but if you have enough for averages to count chickens go though a certain laying cycle. After they mature and start laying as pullets they lay really well until their first adult molt. Often but not always, especially if they are production breeds, the pullets will lay through their first winter and not molt until the following fall. Then after their first adult molt and before their second adult molt they also lay really well. Then after their second adult molt and every adult molt after that production drops. For some individuals it's not much of a drop, for some it can be pretty dramatic. Some hens only lay 3 eggs a week at their best, some lay 6 to 7 a week. It's hard to say exactly how much the production will drop but it is typically pretty noticeable.
Commercial operations typically replace them when they start their second adult molt. Their profit margins are so thin they can't afford to feed them through the molt for the reduced production. Many of us follow that general example but some on here keep them longer, even if their goal is mainly eggs. I knew a man that bought a couple of dozen commercial operations culls for that second molt (really cheaply) and fed them through that molt. He was happy with the production and would eat them at the end of that laying cycle, then get more. There are always different ways to do these things.
My goals are more about meat and just goofing around with genetics, not that serious abut it like someone breeding for show. While hatching eggs are really important the eating eggs are just a nice sidelight. It is nice to have fresh eggs to eat during the winter. Some people freeze eggs when they have a surplus to cover them in winter but I don't.
The way I do it is that I determine the size of my laying/breeding flock, 6 to 8 hens for me, and hatch replacements every year. I typically keep my 4 best (according to my goals) out of the pullets so I don't eat the excess until they are old enough to evaluate. For me that is usually 8 months old. The excess cockerels go to the freezer much earlier. I also overwinter what is left of the four pullets I kept the previous year. Sometimes things happen to some of them, sometimes one or two don't meet my criteria and they go into the freezer early. The ones left from the ones I overwintered the previous year go to the freezer when they begin to molt.
With this rotation I typically have some pullets laying through winter and 6 to 8 hens laying through the next laying season. When the new pullets start laying in late summer/fall I'm pretty swamped with eggs until I reduce to my overwinter flock.
How often I rotate roosters depends on where I am in my genetic goals. I sometimes keep the same rooster for two years but often swap them out each year. Dad kept his for three to four years.
Should I breed from my current stock?
What results do you get when you breed from your current flock? If the offspring have defects it might be best to start over, there is probably a recessive gene in your flock you don't need to keep. Recessives can be hard to get rid of. But that is pretty rare. Even if one shows up if you select your best (according to your goals) to breed and do not allow the rejects to breed, you can usually take care of this.
A typical model that has been used for thousands of years on small farms is to keep your own replacement roosters from what you hatch for 4 or 5 generations. Then you bring in a new rooster to inject genetic diversity. Keep your hens and pullets. The more chickens you have the more generations you can go, the genetics are more mixed up.
There are lots of different ways to go about this. I don't know what is the best way for you to go about this. Good luck however you go about it.
