A Black Sex Link rooster is split for barring. He will give a barred gene to half his offspring, whether male or female. A barred hen will give a barred gene to all her sons and will not give a barred gene to her daughters. Barring is a sex-linked gene. From the hen, it goes to the boys and not to the girls. So any boys from that cross, BSL rooster over a barred hen, will get a barred gene from their mother and may or may not get a barred gene from their father. Half the boys will be double barred and half will be single barred.
With a BSL rooster over a not-barred hen, half the offspring of either sex will be barred and half will not. Since the mother gives her daughter nothing, all the barring has to come from the father for the girls. Since the father is split for barring, half the girls and half the boys will be barred and half will be not-barred. And half should be male, half female.
These are just odds for each individual chick. You have to hatch enough chicks for the odds to mean anything. For example I hatched 21 chicks this past spring. About half should be female, right. Nope 14 female and 7 male. 21 chicks is not nearly enough for the odds to mean a lot.
If you look at the first post in this thread you will see the chart that shows there are many different roosters can be used to make a Black Sex Link. There are also some other combinations that will work. Without knowing the parentage of the BSL rooster, you don’t know what his offspring might look like. It gets even more complicated. Some BSL’s are made by crossing specific breeds but some come from the commercial laying industry hybrids. You really don’t know what the parentage looks like and those are 4-way crosses, not 2-way.
But many hatcheries use a red rooster over a barred hen that has Extended Black, so let’s work with that. It’s as good a guess as any and better than some.
With a red father and a black barred mother, the BSL rooster will be split for black and one of the alleles that give red roosters. So he might give a “red” gene to his offspring or he might give a black. It’s 50-50. (That red gene might be Wheaten, Duckwing, or Partridge.) To make it worse, the red father will contribute a gold gene but many black barred hens will give their son a silver, so the BSL rooster is probably/possibly split for gold/silver as well as red/black. There is a 50-50 chance of either gene going to any of his offspring.
So assuming your BSL rooster is split for barred, red/black, and gold/silver: (Get the idea this may get messy?)
Delaware hens are barred, silver (both dominant sex linked genes) and probably Wheaten. So the boys from that cross will all be barred and will all have silver from their mother. They are 50-50 on red-black, barred, and gold/silver from their father. The Delaware should also contribute a dominant Columbia gene, so half of the boys should look a lot like a Delaware. Half the boys will be black barred. Half the girls will be black, split barred and not barred. ¼ will be red, split barred, not barred. ¼ should be white, split barred, not barred. You can see the barred on any dark tail or neck feathers.
I have no idea what you will get from the White Leghorn. I don’t know if that is dominant or recessive white. I have no idea what might be hiding under that white.
The red sex link is a cross. She should be pure for red and contribute a gold gene to her sons. So with that BSL rooster, half the offspring of both sexes should be barred. Half should be black. With the rooster split for gold/silver ¼ should be red, ¼ should be white but probably with pattern feathers, maybe on the tail, wings, or neck for both red and white. That depends on the parentage.
The BSL hen is a cross, so let’s assume she is similar to the BSL rooster. We are assuming she is split for red/black. Of the sex-linked genes has a gold from her father and is not barred. So ¾ of the offspring of both sexes will be black-based and ¼ will be red-based. But half those red-based will see silver from the rooster so only 1/8 will be red and 1/8 will be white. Half of those of either sex will be barred and half won’t.
I have no idea how a dutch bantam is colored or the genetic make-up.
The Speckled Sussex has red, gold, and not-barred. The mottling gene that causes the speckling is a recessive gene so it will not show in the first generation. So with the BSL rooster, half the offspring will be black, ¼ red, and ¼ white. Half will be barred.
I’m just guessing on the parentage of your sex links. If I guessed wrong all this is wrong. When you talk about a red or black sex link you are not really being very specific about their genetics other than the sex linked traits. And a whole lot of stuff can be hidden under either black or white so you don’t know what is lurking under there. For example, your White Leghorn could be carrying barred for all we know. That would have an effect on the boys.
You are dealing with a lot of crosses here, the BSL rooster but also some hens. When you cross crosses you can get a real strange mix. I may call something red but that red could be many different shades. You are likely to get a wide range of patterns. I like crossing crosses. You never know what you will get. All I know for sure from that is that you are highly likely to get a bunch of different looking chickens unless the father of that BSP Rooster happened to be Black. Then you will probably get a whole lot of black chickens but some could be white. You really need to know the parentage to even get a clue and even then you will probably get some surprises.
I read this twice, took a break, and reread it. Hopefully I got the mistakes out. Good luck and enjoy.