Why do you want to redye black shorts (fading, showing white bits...)? Are they all made of the same material (eg. they might have a zipper you want the same colour, sewing thread of a different sort (polyester vs cotton) or buttons)? Is there anything on them you don't want to dye (some embroidery)?
Black is a notorious colour for dyeing. Different fabrics require different dyes - silk/wool/cotton/polyester are all different - which don't react the same way to other fabrics. However, fabric paints colour everything, and some (like dye-na-flow) don't change then hand of the fabric. If your shorts were painted originally (showing white bits) rather than dyed (fading), a dye (which is a chemical bond between the fabric and the dye) probably won't take because the paint is actually covering the fabric.
Dharma Trading have good supplies. RIT is OK