I had looked this up myself in the past as I have chocolates, and I have paints, so thought about breeding them to make chocolate paints.
I found
the thread I had found back then, and someone interestingly attached the same chart. There is some misinformation there, but it's cleared up.
Blacks can't be split to paint, or carry a paint gene. When a black is bred to a
dominate white, the chicks will be 100% paint, but by the combination of the two, not due to anything from the black one.
Your black silkie hen to a chocolate roo is going to be Chocolate pullets and Black split to Chocolate cockerels, no matter if your black hen came from a paint parent or not.