Yes, a black rooster over a blue hen can create a splash.
No, a black rooster can never produce a splash chick.
Splash means the chick has two blue genes, one inherited from each parent. A blue hen can give a blue gene to her chicks. But a black rooster has no blue gene, so he cannot give one to the chick, so the chick cannot be splash.
I have and black silkie roo and blue and black hens. What color are these chick? Blue? Splash? I also got a partridge chick, which surprises me, since I don't have any partridge. Can a black roo and blue hen have a splash chick?
I am not good at recognizing many chick colors, so I do not have an opinion on what colors they actually are.
Regarding genetic possibilities:
No, a black rooster cannot produce a splash chick, no matter what color of hen he is mated with.
Some blue chickens can be very dark and may look black. If your rooster is actually dark blue instead of black, he could produce splash chicks when mated with a blue hen.
Some blue chickens can be very light, so they may look like splash or white chicks when they are young. This is one possible explanation for your chick that looks splash, even if the rooster really is black.
Black is dominant over many other colors, so it is sometimes possible to have a black chicken that carries the genes for partridge, or lavender, or white, or some other colors. If a hen and a rooster are each carrying the genes for one of those other colors, they can produce some chicks that show that color.
Hens can store sperm for at least a week after mating with a particular rooster, and sometimes for three weeks or even longer. Did any of the hens have contact with another rooster in the month before you collected eggs for hatching? Or is there any chance that you mixed up eggs and some of the chicks came from different hens? Sometimes unexpected colors in chicks are caused by mixups about who the parents actually are.
In many cases, chicks with unexpected colors will be less puzzling when they grow some feathers. Sometimes their adult color is normal and they just looked strange when young. Other times they still have a color you did not expect, but at least you have a better idea what color it is, which can help with figuring out what happened.
