That is a good question. The answer is that it will probably not cause problems. Practically all breeds were developed and practically all grand champion chickens are developed by inbreeding. That method has been used in backyard chicken flocks for thousands of years.
The key is how good a rooster is he? If he has genetic defects or susceptibility to disease, he will pass that on to his offspring. If he is bred back to his daughters, any genetic weakness will be enhanced, but so will any genetic strengths. If you select your breeders with some care, you will probably be OK.
I can't give you any guarantees but a whole lot of people on this forum do what you are talking about. Usually it works out OK.
One problem is that you can lose genetic diversity over the generations. If you have several different roosters in the flock and several different hens, it is not that much of a problem for many generations. If you really know what to look for or follow certain techniques, like spiral breeding, it is not a huge problem. But for most of us with out skill levels, it is probably a good idea to bring in new blood every four or five generations. And, of course, watch the offspring. If you start to notice problems, don't wait to bring in new blood.
