Inbreeding is not at all uncommon. Most small farm families from the day this country was setled had flocks that inbred a lot, bringing in new blood occasionally but going for several chicken generations without bringing in any new blood. They raised a lot of families off those eggs and meat.
What happens depends on the genetics of your chickens. It's possible your chickens have some bad trait that will come out if you inbreed them. Remember that because something is possible does not mean it will absolutely without a shadow of a doubt 100% of the time happen each and every time. Don't panic needlessly because something is possible.
If you breed them and 100% of the chicks show a problem, you don't just need a new rooster, you need a totally new flock. That really does not happen often. If some of the chicks have a problem, don't allow those to breed. Don't fall into the trap that Crippled Henrietta is such a sweet chicken, I want her chicks. You really do need to be pretty ruthless about this if you see any problems or you will soon have a flock that has nothing but problems.
Breeders have certain techniques to help avoid severe inbreeding problems, such as spiral breeding. A good breeder can go for a long long time without bringing in new blood. That's how every breed has been developed.
For most of us that are not going to keep three separate flocks and set up breeding pens for specific rooster/hen matches, it is probably a pretty good idea to bring in a new rooster every four or five generations just to keep the genetic diversity up. Just watch your chickens. As long as they are healthy and productive, you are OK.