To make a red sex link chick the father has to have gold, the mother silver, and the down color has to be such that you can see the difference between the reddish and yellow down. By definition a red sex link hen is gold, not silver, so they do not work. Your Black Australorp rooster might have silver, he might have red. Usually they are silver but there is no guarantee on that. With a Black Sex Link hen you will not be able to see any difference in difference in the down color if it is even there.
If any of your hens are barred you probably can make a black sex link with a Black Australorp rooster. For a chick to be a black sex link the father cannot be barred and the mother has to be barred plus you have to have the down color so you can see the spot. There area few hens you won't be able to see the spot with a BA rooster but not many. By definition. black sex link hens are not barred so they will not work. Are your red sex link hens barred?
You can only make sex links when the father has both genes at that gene pair to be the recessive of the sex linked gene and the mother has the dominant sex linked gene. Once you have made sex links the genetics are mixed up so it does not work in the second generation. You cannot use sex links to make sex links. The only exception I can think of to that is if you have barred red sex link hens you might be able to make black sex links with them but I don't know any hatchery that sells barred red sex link pullets.
