There are lots of different ways to get black sex links, but there is absolutely no link between black sex links and blue eggs. There is no real link with black legs and blue eggs. Some, not all but some, blue or green egg layers tend to have slate colored legs, but mine had yellow legs. The genetics between the barring that makes a black sex link (lack of barring in the hen), the leg color, and the egg shell color are unrelated.
I'd very much expect brown eggs from black sex links.