With the colors you have:
I’m still learning genetics and colors.
How do you get mottled or splash orpingtons?
I'll answer differently.
The mottled gene is a recessive gene that puts a white tip on some feathers. It can look differently on different colors and does not show itself on all feathers. The symbol for mottling is "mo" with the lower case showing it is a recessive gene. Since it is recessive you have to have both genes at that gene pair to be the mottling gene to see it. If one gene is "mottling" and one is "not-mottling" you won't see it.
If you breed two mottled chickens all of the offspring will be mottled because they have to have two mottling genes at that gene pair. (mo,mo) x (mo,mo) has to give you (mo,mo)
If you breed a mottled chicken to a not-mottled chick that has one mottled gene half the offspring will get two mottled genes and it will show. (mo,mo) x (MO,mo) gives you about half (Mo,mo) where it will not show or (mo,mo) where it will.
If you breed a mottled chicken (mo,mo)to a not-mottled chicken that is (MO,MO) you will get all (Mo,mo) chicks and it will not show. But if you cross a (Mo,mo) to a (Mo,mo) about 1/4 will be (Mo,Mo) and it will show.
The genetics to make a splash chicken use the Blue gene (symbol "Bl"). Instead of dominant or recessive this gene is partially dominant but you still show it as upper case. Not-Blue is lower case "bl". This gene modifies what normally would be Black, it doesn't affect white or red feathers. If both genes at that gene pair are Blue (Bl,Bl) you get a Splash chicken. If one gene is Blue and one is the not-Blue gene then you get a Blue chicken (Bl,bl). If both genes are not-Blue (bl,bl) you default to a black chicken. One interesting thing is that if the chicken would normally be solid black without the Blue gene you can get a solid Blue or Splash chicken. If you have a chicken that is normally white or red but has a black tail you get a white or red chicken with a Splash or Blue tail. It only affects the feathers that would normally be black.
I don't know if this is the type of genetic discussion you were looking for. I probably made it sound more complicated than it is. Hopefuy between this and NatJ's you can work it out. Any questions, please ask.
if you are that interested in genetics you might look up Punnett Squares if you don't already know about them. That's how you look at the possible crosses.