Normally, yes. Inbreeding (parents to siblings, siblings to siblings, cousins to cousins) is how all breeds were developed. It's how champions of chicken shows are developed and the flock maintained. Inbreeding is not as horrible as some think.
The trick though is to choose which you allow to mate. If a chicken has a deformity or a trait you don't want, don't breed it. If a chicken has a crossed beak or weird toes, don't breed it. Or basically any traits you don't want.
Over the generations you can develop a lack of genetic diversity to the point the chickens become less productive or healthy. The more roosters and hens in your flock the slower that process. A standard method of handling this on small farms for the past few thousand years is to bring in a new rooster every now and then to reset genetic diversity. It's hard to say exactly how many generations because of the different ways the flocks were managed and how many roosters and hens they kept, but with just one rooster and maybe 20 hens in a flock they might go five generations.
This chart explains line breeding and how much of the same "blood" is in each crossing.
When selectively done it works. If both mother and son are close to ideal, pair them together and hatch everything she lays in an incubator. The best son from that goes to the sisters of the first rooster. If you can develop 2 groups to do this method with, at that 6th generation is when you can switch them and repeat.
It takes quite a bit of time to establish a decent sized breeding group. If you use every bird you have and don't separate them by compatible traits or if you use birds who have flaws and breed them to birds with worse flaws... you'll end up feeling like you need a new flock in no time.
With only one rooster, you'll need to know which eggs you're hatching and tag their legs or toe punch, so that you know who's from who for that next hatch. You'll want to grow out at least 10 roosters to pick the best son from.
You obviously haven't met my relatives.
Father and daughter and mother to son is what tends to happen here without intervention on my part.
How many iterations was one of the few questions I've asked on BYC and apparently up to 7 generations is considered okay.