The barred rock cockerel should be pure for the barred gene and give a copy od barring to all his offspring. Since it is dominant all his offspring, male and female, will be barred. Definitely not sex-linked.
A whole lot of different roosters could be used to make a black sex link pullet with a barred mother so the genes that make up the color can be pretty mixed. They are certainly unknown. There are also different genetic ways to make black. The odds are extremely high your chicks will be either black barred or black barred with some red leakage (a few red feathers showing through), but weird things can happen when you use a crossbreed like that black sex link pullet. You can get some surprises, either in the chick down color or the adult feathering. So expect black chicks but don’t be shocked if something strange happens to some.