There are a few products that will be most helpful in painting your silk skirt. The range of colors available in fabric paints can be really dismal.
Textile medium is available in several different brands, found in most art and craft supply stores.
It alters the composition of the paint to make it bond better with fabric, and makes the painted garment washable. It doesn't work well on synthetics, espescially polyester, probably because they're not as porous as natural fibers. There are also special paints for silk painting, but they're a bit pricey. Another product I love is paint stop. It allows you to control the flow of the paint, as paint tends to run on silk.