Fabrico stamp pads (they may have changed the brandname to Versacraft) are made for stamping fabric. Acrylic paints can be mixed with a conditioner which makes the paint *work* on fabrics. Jacquard has a line of products just for fabrics called Dye-na-flow.
Look in the gallery - there is the cutest pajamas that have been stamped (not my work!- I just wish!)
Gallery at Splitcoaststampers
Clearly this is the person (or her friend who made them) is an expert! Hopefully she will chime in on how it was done.