It sounds as if the companies, such as GAP, use products made of things, some of which are harvested by slave children. Gap, for instance, sells clothes. I would guess than they pay companies to make the clothes, those companies buy cloth from other companies who may buy cotton from sources that use slave labor to pick the cotton. The start of the process is so far removed from the place where we buy the end product that there isn't a good way to tell what the story of that product is and who was involved.
Buy "Fair Trade", and I'd guess there's less of a chance forced labor was involved. It would be a good idea to have some sort of world-wide oversight on labor practices, but we're a long way from being able to do that. It may be easier to find some registry of "good" companies, and deal only with them.