I am not anywhere an expert on the genetics of chickens. I'm just somebody trying to maintain a sustainable flock with the main goals of them doing a lot of free ranging, breed my own replacement layers and roosters, going mainly for meat but with egg production reasonably important. A broody would be nice too but I know I'll be running the incubator a couple of times a year. I'll give my opinion and hope to get corrected where I am way off.
I'm sure there are different business models for the hatcheries. Some probably keep their own flocks or have exclusive agreeements with people for hatching eggs. I suspect a lot of them buy hatching eggs from the same flock, especially for some of the rarer breeds. There is always a chance that you can get full blooded brothers and sisters from a hatchery, but I think the odds of you getting closely related chicks from a hatchery are pretty slim. They hatch out a lot of eggs. They keep one rooster for every ten hens. You are probably OK as a starting point with stock all from the same hatchery. If you are really concerned about them being inbred, start with a mix of breeds. Unless I misread your goals, mutts should do you just fine.
If you are going to go for a sustainable flock without adding outside blood, you need to learn a lot more than I know about genetics and what you are looking for. Since you are not showing, color of the legs or number of points on a comb are not important to you. I'm guessing egg production and probably meat are important. Also important are them staying healthy, that they lay fertile eggs, and don't develop any deformities that interfere with your goals or their ability to sustain themselves. To achieve this, I think you are going to have to hatch out a whole lot of chicks and cull mercilessly. You are going to have to keep a fair number of chickens to form your breeding stock. Keeping one rooster and ten hens won't do it. I don't know what the magic numbers are, but you need enough diversity in your breeding stock to weed out bad traits if they show up. Unless you seriously get into it, I think you are going to have to add outside blood fairly regularly.
I don't know what fairly regularly will mean to you. It will depend on how good you are at culling, how many chicks you hatch every year, how big your flock is, and somewhat how lucky you are in what you hatch. I like to add by getting hatching eggs and raise my own. I think getting NPIP certified hatching eggs is the safest way to add to the flock from a disease perspective, but there are plenty of other options.
You can get hatching eggs or new live stock many different ways, hatcheries, neighbors, people on this site, chicken meets, chicken shows, Craigslist, whatever. To me, probably the best way is to get eggs or chicks from a breeder. I have a tremendous amount of respect for the true breeders, the ones that put a lot of time, effort, and money into achieving their goals. But not all "breeders" are created equal. Some people will buy a bunch of chicks from a hatchery and sell the offspring as pureblooded chickens. Those are no better than hatchery chicks and may be worse if they don't know what they are doing or don't hatch out enough and cull properly. Some people are developing lines that are not in any way related to what you are trying to do. I met someone a couple of years ago that was trying to develop a line of chickens that has an extra toe. One of his chicks hatched with an extra toe so he thought it would be cool to develop a line with an extra toe. He also has some lines he is trying to breed to the standards and he is trying to develop some different colors. Someone breeding to standards and trying to develop a grand champion may not be your best bet. To them, the sharpness of the feather pattern is probably more important than how well they lay eggs. Many times, chickens bred to standards are going to be superior to hatchery chicks, but not always. It depends on your goals. If eggs are your sole goal, hatchery chicks have been bred with eggs in mind. I think getting hatching eggs from breeders is the best way to improve your stock, but you need to talk to the breeder and let them know what your goals are. The good honest ones will tell you if their line of chickens will help you meet your goals.
These are some of my thoughts on getting and sustaining a flock. I'm no expert but maybe you can get something helpful from this.
