I don't know why it doesn't happen more often that a chicken is in the wrong place at the wrong time and gets a load dropped on them.
Yes, you can wash your Silkie. I like children's mild bubble bath liquid. (Mr Bubble) Fill a wash tub with warm water and a tiny dash of the liquid bubble bath. Have a tub of clean warm rinse water ready. A couple of absorbent bath towel ready.
Gently splash the soapy water onto your Silkie until the soil loosens. Do not rub or scrub the feathers. If the soil is stubborn, take a wash cloth and gently swipe soapy water in one direction across the dirty feathers.
Once the soil is washed away, do the rinse cycle.
Plop the soggy chicken in a dry towel and squeeze out the excess water like you would when washing a delicate and very expensive wool sweater. Then use the second dry towel to do more patting and drying, careful not to scrub and rub the feathers.
If you have a hair dryer, use it to further dry the Silkie. Chickens love to be blow dried. It will make up for the indignity of the bath.