I did see that one about the Rhode Island Red bantam with the unusual voice, but I do not know anything about what genetics might be involved, or if it even caused by genes at all.
At a very basic level, for any trait you want to reproduce:
--hatch chicks from the chicken that has the trait, and see if they have it. (Generally works if the trait is caused by a dominant gene, or sometimes works if the trait is caused by two or three dominant genes.)
--If no chicks have the trait, breed a chick back to the parent that does have the trait, and see if that produces any chicks with the trait. (Generally works if the trait is caused by a single recessive gene, or if you hatch large numbers of chicks it can work for a trait caused by two or three recessive genes. If the trait requires both recessive and dominant genes, this method will typically work for that too, but the more genes involved, the more chicks you need to hatch to get some that show the trait.)
If that still does not give any chicks with the trait, either it is genetically complicated (more than about 2 or 3 genes involved), or it is not controlled by genes at all (like if you had a chicken with unusually short toes because they lost the tips to frostbite: they do not carry genes for shorter-than-usual toes.)