For your edification, (edibilty education), the modified goats are milked by the researchers, not their offspring. The spider silk is separated from the milk, which is then presumably offered to the kids.
They wouldn't let the goats eat the prized spider silk. They want to save it for the worms.
Actually, I'm not sure those worms would want to tangle with spider silk, unless they want to floss with it.
Silk dental floss, hmmm....