I am by no means any sort of an expert, but from my last years worth of researching chickens, here's my understanding.  Inbreeding can be a good thing or a bad thing depending on several factors.  One of the most common reasons to intentionally inbreed is to improve the selected breed and eliminate flaws that an outside specimen can introduce.  At the same time, it limits the available gene pool and can cause the weaker traits to be displayed, often times causing the offspring to be less hardy.  It's really a double-edged sword and you have to decide what is best for you.
 
Personally, knowing that I probably wouldn't be breeding more than between the initial siblings or even children to parent, I would be ok with it.  At that point, all of the first generation offspring will be for either eggs or meat.  Especially the ones set aside for meat, reaching a fertile mating age is highly unlikely.  Every few years, I would probably want to replace a few members of my flock with some outside chicks and allow those to be introduced into the breeding program, just to ensure a bit of diversity.  I'm talking every two or three years, though.  We are talking a very minimal selection of inbreeding here.  Problems tend to arise after several generations or more.
 
If a person is serious about their breeding program, which is the type of person you should be wanting to get your flock from, I would presume they will have multiple lines going and be able to take a cockerel from one line and give you hens from the other line.  With cockerels being significantly less desirable, they may even give you a few just to avoid culling them.
 
 
Sonoran there, is a true breeder and has some absolutely beautiful stock.  She can give the best advise from the aspect of genetics.  Her goals are significantly different than yours, though.  We have two of her Silkies (a cockerel and pullet that is approaching a year old and hasn't laid) and, even though I can not stand the looks of them personally, I can recognize and admit when there is a high quality to them.  My wife loves them dearly and I've been threatened with my life several times when I mentioned getting rid of them.  I have seen some absolutely horrible stock being passed off as a Silkie, so the difference is amazing.