Chickens probably do not line breed very well.
They have about twice the genetic load as other animals like humans. The genetic load is just a measure of the lethal equivalents in a genome. Humans have one of about 2.5. This just means you have the equivalent of about 5 recessive lethal genes in your genome. This is why brothers and sisters should not mate because they share half their genetic loads and recessive lethals or detrimental genes can be expressed in the progeny of inbred matings.
Chickens have a genetic load of around 6. Nearly all inbred lines generated by full sib (Brother/Sister) matings fail after just three full sib matings. Once the inbreeding coefficient goes over 0.375 the lines tend to fail to reproduce one male and one female to continue the line.
So inbreeding in chickens is not a very good thing to do a lot of if you are un-aware of the downside.
The reason people like to line breed is that it is the fastest way to select for type that is caused by a complex interaction of genes. If you have a superior animal the fastest way to increase the frequency of the superior genes in your line is to line breed.
Line breeding is just when you take the superior parent (hen or rooster) and cross the progeny back to the parent (father to daughter or mother to son). You then take the superior parent and again cross it to its new offspring from the inbred mating. You repeat this until infertility becomes a problem or the parent dies.
You can select other progeny that presumably will be better than average for your flock to breed in non inbred matings or to other close relatives to try and set the good traits in your line.
The reason that this works is that in the first mating the progeny have only half the sires genes. We say that the inbreeding coefficient (F) is 0 because none of the non inbred progeny can have both the alleles from the sire. When the sire is crossed to his daughter F = 0.25 this means that 25% of the genes of the progeny are identical by descent (both alleles of a gene come from the sire) and 75% of the total genome comes from the superior parent. These first generation inbred progeny have been fixed for 25% of the sires genes. With the next inbred mating of sire to grand daughter F = 0.375 and 87.5% of the total genome. Mating to his great grand daughter F = 0.438 and 93.8% of the total genome comes from the superior sire. After this inbred mating the gain is much less (the next inbred mating results in F = 4.69 and 96.9% of the total genome) and the birds are getting pretty old, so you can pick the best son and start it over again.
Line breeding can produce very rapid gains in the quality of your line for certain traits, but nearly always results in a degeneration of the reproductive capacity of your line and you end up outcrossing and starting over. For a few generations it can give you some outstanding birds at a higher frequency than you would get by not inbreeding, but there is no such thing as a free lunch. This is why commercial breeding companies try to avoid inbreeding and concentrate on improving the whole population. The gains are not as dramatic, but they don't fall on their faces as often.
I don't know what the best breeding scheme is. You should do a little inbreeding but not a whole lot and if you inbreed I'd recommend parent to offspring inbreeding because all the genes that become homozygous by descent come from the superior parent. If you brother sister inbreed you get about the same amount of inbreeding (0.25, 0.375, 0.5, 0.594, 0.672.) for the first few generations, but the genes that become homozygous by descent come from the superior parent and the inferior parent. So if you brother-sister mate you are not only fixing genes from the good parent, but from the not so good parent too.
Maybe the best advice is that if you inbreed always use a superior animal for the mating. If you do not you are just increasing the bad genes in your line.
Any mating between related individuals is inbreeding. Line breeding and full sib mating cause the same amount of inbreeding for the first two inbred generations. Theoretically line breeding and full sib matings should have the same detrimental results for the first two inbred generations. Full-sib mating would be more detrimental for the 3rd and subsequent inbred generations.
The difference is that all the inbreeding comes from the superior parent in line breeding, but half the inbreeding comes from the inferior parent in full-sib matings. This is why I'd recommend inbred matings involving only birds that you think are good enough to warrent it.
I have line bred for years and thats the only way to produce better birds.
http://www.castlefarmeggs.co.uk