It is difficult to predict what you might get. I'm definitely not an expert but can share some insight based on my understanding (just take it with a grain of salt as I am still learning too).
White silkies are usually recessive white but can also be dominant white.
If your rooster is recessive white which is probably more likely than dominant white it's really hard to say what you might get. The recessive white can hide all sorts of colors. I've heard partridge is one of the more common ones though. If your boy is partridge under the white you'll likely hatch black chicks with possible leakage. Of course if he is something else under the white you might have different results like possible blue chicks etc. Unless your black hen happens to be carrying a recessive white gene this pairing should not result in any white chicks. With this pairing you also shouldn't be able to get any splash chicks (this is assuming your black hen is definitely black and not dark blue which can sometimes look black).
If your rooster is dominant white than paired with the black hen you'll likely get paint and black chicks with possible leakage. Sometimes the chicks inheriting the dominant white will not get the typical paint spots and will appear white even though they are heterozygous for dominant white (lacking two copies of it). With dominant white it is probably more likely your rooster is black based under the white but there is a possibility of splash or blue as well which could give you the chance of blue based paint chicks and blue chicks too.
If your black hen happens to be carrying some recessive genes for partridge/penciling and your rooster does as well there is a chance of getting some partridge like chicks too. If the rooster is dominant white and this is the case their would also be a chance of getting some sort of red pyle like chicks too.
All in all guessing what you'll get is really tough. On the upside you'll likely gain more insight into the parents genetics depending on what kind colors the chicks turn out to be.