Are you sure it is an Ameraucana rooster and not an EE? If it is an Ameraucana, which recognized official color and pattern?
Without knowing anything about the Ameraucana, I really can’t help you much, but maybe a little. And that will come with a lot of “if’s”.
If your rooster has the right genetics so you can see the spot and if the rooster is not barred, a cross with the Barred Rock hens will be black sex links. The males will have a spot on their head where the females will not.
The cross with the Ameraucana hens depends in the colors and patterns of them versus him. Without knowing that information, I have no idea.
Your Gold Buff hens are crosses. You will not get sex links from them. Without knowing his color and pattern, I really don’t know what you might get.
You will not get sex links with your Black Australorps. It depends on his genetics, but the chicks will probably be black. Probably.
A true Ameraucana will be pure for the blue egg gene. That means every one of his offspring will get a copy of that gene. The blue egg gene is dominant over the white egg gene, so all his offspring will lay either blue or green eggs. If he is not pure, then he may have two copies, one copy, or no copies of the blue egg gene. This means if he is not pure, his offspring might or might not get a copy of the blue egg gene.
All eggs are either base blue or base white. If there is no brown involved, the eggs will be either blue or white. If there is brown involved, then the eggs will be either brown or green. A true Ameraucana will not have any brown involved so the eggs will be blue.
Your Barred Rock, Gold Buff, and Black Australorp all lay brown eggs. So a cross with an Ameraucana rooster will result in a pullet that lays green eggs. A cross with an Ameraucana will result in blue eggs. If the Ameraucana are not pure, then you might get blue, green, or brown eggs from the Ameraucana cross.
