Although many people will offer implausible causes for FCK (such as queens lying on heat pads or heated floors during pregnancy) all of these theories have been disproved. It is possible that a mating liable to produce FCK will have that liability increased by external conditions, but it can be clearly seen that some cats will throw FCK and some will not unless mated to another cat which throws the condition. Unfortunately, the genetic picture is not clear - a cat cannot be described as either a carrier or not a carrier. We know that this condition is genetic, but it seems to be polygenic, which makes it much more difficult to locate. I have heard from two breeders who did repeat matings, but only had FCK kittens in one litter.
Some lines throw FCK far more than others, and some studs or queens are well known for it, and so you avoid them in your breeding lines if you can. Virtually all studs in all breeds have thrown one at some time or another (because of the numbers of kittens they sire), so it's unavoidable, and abandoning ALL lines that have thrown FCK would be incredibly damaging to any breed as it would limit the gene pool far too much. It seems that either sire or dam, or both, may carry the genes that trigger the condition, but having it manifest in a litter of kittens can rely on combinations of environment (whether the queen is healthy and produces a lot of milk) and other factors. The main thing to avoid is having a known serious FCK carrier in your pedigrees, but also to avoid having the same cats in the pedigrees too much as well. FCK appears much more often with inbred lines.
There is also no doubt in my mind that sometimes FCK appears without any apparent genetic component. I suspect that it is a condition that manifests as a result of any number of causal factors. This is a bit like a human running a temperature: we get a temperature as a result of a huge number of illnesses, but the temperature is always the same, and it is just a sign that something is wrong, and is caused by an underlying illness. It looks as if single cases of FCK can appear a bit like a temperature - the outward sign of something being wrong, so it can be the result of another problem, as well as a problem in itself.
Unfortunately, some stud owners continue to run studs who have thrown a lot of complete litters of FCK kittens. I have personal experience of a stud owner who said categorically that her cat had not thrown any, only to find after my kittens were born that he had had two complete litters and the stud owner knew about them: I talked to the owner of the queen that had had these kittens, so there was no question of the information being just malicious gossip. This stud was widely used as he was a UK Grand Champion: when 'clean' lines were mated to him the kittens were generally healthy, but kittens bred from those offspring nearly always develop FCK. Fortunately my kittens were all completely healthy, but I knew that they had at least a 50/50 chance of carrying FCK, and so I did not feel I could keep a kitten from the litter to continue my lines. I was very sorry to lose this line, as this unwitting 'test' mating showed that my line was not susceptible to FCK. Unfortunately I could not mate the queen again to get a breeding girl from her, and she had to be neutered. Needless to say, I was more angry than I care to remember!
It seems that there are numerous genetic markers that must be present in order for the condition to arise: if a cat has many of these markers then most of the offspring will have flat chests. If mated to another cat with a high level of markers, then all kittens in a litter will be flat. Single flat kittens may suggest that one of the parents carries a significant number of markers that were mitigated by the other parent being relatively free of them OR that there is an environmental rather than a genetic reason for the condition developing.
FCK can be affected by the situation of the queen: any adverse event during pregnancy (including poor nutrition) can render a queen liable to produce FCKs if she carries a small number of 'markers', while a better environment may prevent the condition from developing. If you have just one flat-chested kitten in a litter then the causes could be environmental more than genetic (see paragraph below), but maybe using a different stud would be safer for breeding next time. It seems to be rare to get a whole litter of flat chests unless both parents are strong carriers of the genetic cause, so it would be advisable to abandon a breeding line that produced whole FCK litters. Single flat kittens in a litter, though indicating a risk in the lines, may not be such a serious problem and it may be only one parent who is the cause, assuming there is no environmental factor. Many breeders prefer to avoid any incidence of FCK in the lines they are using if they possibly can, even though this may severely limit their gene pool (and there are many dangers for a breed in following this course), but sometimes a kitten will turn up in a line that was thought to be clear. It is a matter for each breeder to weigh up the factors of FCK risk and limiting their gene pool to a dangerous degree, and I'm not going to criticise the decisions individual breeders make.
There may possibly be physical reasons why FCK may occur that have nothing to do with genetics or the bloodlines: if a queen was ill during pregnancy, or had to have antibiotics; if the queen had a fall during pregnancy that might have knocked one of the fetuses. Also, if one kitten is getting less good milk than the others: sometimes a queen has one teat that does not produce as much milk as the others, and the kitten who gets this teat may go flat from vitamin deficiency or lack of good nutrition (if that is one of the causes). Sometimes with very big litters the smallest may be flat, though I have had litters of 8 and 9 with no problems at all (and the queen lay on top of the radiator all through every pregnancy without producing a single flattie), so I'm not sure that is a legitimate cause. Some people will look for any excuse to say it's not their bloodlines, particularly if the cats they breed are very good show quality, or if they are very attached to their bloodlines for other reasons. All you can do is ask the breeder if you are looking for a stud or breeding queen. FCK CANNOT be caused by your queen sleeping on a heat pad or other heated surface while pregnant. I have had 15 Siamese, Burmese and Tonkinese queens over the years who have spent their entire pregnancies (to various studs) stretched out along the tops of radiators or sitting on top of an AGA, and never had a single flat chest. Veterinary studies have now comprehensively RULED OUT sleeping on heated surfaces as a cause of FCK, though originally when the syndrome was first identified it was suggested that it might be one possible cause.