The answer is not as simple as some people would have you believe. Inbreeding chickens with certain traits is how all the modern breeds were developed, even mutations because you had to breed the descendents of the mutated bird to fix the trait. Inbreeding will strengthen their traits, whether you consider the traits being enhanced good or bad. If you select the chickens that have the traits you want and breed them, those traits will be enhanced. You might see traits you don't want so you need to not allow those chickens to breed. Some of the traits you don't want may not be readily evident, such as loss of fertility.
Inbreeding does limit genetic diversity. That's how the good traits get enhanced but it also raises the chances of something bad happening, maybe the become less hardy. It is usually a good idea to introduce new blood occasionally. How often depends on what you see developing in your flock. Some people go on a set schedule, like every 4 or 5 generations, but I think it is more important to observe your flock, be flexible, and determine what you do based on what is actually happening within your flock.
I imagine my goals are different that Darkmatter, but I am also breeding my own mutts. To me, size is more important than egg production, so I base a lot of my decision on which chickens to keep to breed based on size. I still want enough egg production so there are some trade-offs. This means I eat the smaller chickens and not the delicious looking tempting larger ones, all else being equal. But every year the ones I eat are getting bigger.
To answer your specific question, you will probably be OK but you will need to look at the offspring and see if they have any deformities or traits you don't want. If they are OK, keep going. If they exhibit traits you don't want, start over.
Good luck!