Well, if we could do DNA testing and ascertain that the bird had the correct genes for the variety, and that they are homozygous whereever possible, that is all you'd need
Unfortunately, the technology isn't there, and the cost is prohibitive to all except possibly Bill Gates.
There is no "correct number of generations." Silkie breeders are about the only ones who throw a fit when a bird doesn't breed true each and every time. Those who raise other breeds expect some surprises and sports.