Gail Damerow describes how to dye chicks while in the eggs, as a way of keeping track of different breedings. For example, you breed hen A and hen B to rooster X, and want to see the difference between hen A's offspring and hen B's. The eggs will incubate together, hatch together, and how will you know which is which?
One method would be to (keeping the eggs separate in the 'bator, maybe hen A's on the left side, hen B's on the right) to dye the embryos of one of the hens. Or dye both sets different colors.
She advised using food coloring, which would not harm the chicks. Dyeing is done around the 11th day, I think she said. It's in The Chicken Health Handbook.
By the time the chicks start to lose the color, they'd be big enough to put identifying leg bands on.
I wouldn't dye chicks for sale, (because of the "disposable" live creature problem) but if you are keeping them anyway, dyeing embryos for ID purposes or to entertain your children wouldn't be a problem, IMO.
The embryos themselves are not even touched with the needle, the dye goes into the fluid portion just inside the membrane, and then you seal the hole with wax. If you are careful, and clean the injection site of the egg, and use a sterile needle, you won't harm the chick.
When I was a child, we got colored chicks every year, and when they grew up they just mixed in with our other chickens.