I have read about spiral breeding and line breeding, but we are not wanting to improve what we have, just sustain what we have.
I assume sustaining what you have is talking about productivity, health, and wellbeing. Sustaining isn't that different from improving. What you are really trying to do is to do is to not let them get worse.
One important component is to not let defective chickens breed. Choose your breeders with care. When you inbreed defective recessive genes can match up. It is not that every chicken has these but some do. Any chicken that has a cross beak, crooked toes, or some other problem should not be allowed to pass those genes on in your flock. This doesn't happen that often but if it does deal with it.
When I select which ones get to breed I try to select hens that lay well and lay egg colors that I want. I try to select for color/patterns and I try to select for behaviors.
The other part of inbreeding is that you can start affecting the general health and productivity of the flock. It's called losing genetic diversity. They may become more susceptible to diseases, produce fewer eggs, lose fertility, things like that. Dad had a flock of one rooster and 25 to 30 hens and kept his own replacements. He could go 4 to 5 generations without these problems showing up. Even without seeing any problems he's bring in a new rooster and restart the genetic diversity clock. I remember him doing that twice when I was growing up. One rooster was a New Hampshire rooster, the other a Dominique.
I can't tell you how many years you can go before you need to bring in a new rooster. That depends a lot on what actual genetics your chickens have to start with.
Do we need to be concerned with our roosters mating with their daughters or brothers and sisters mating?
Nope, not with hens mating with their sons either. Not for a few generations. But only breed your best.