That's more a function of their breed than their feed. Specific breeds produce the different shell colors, such as Americanas, Araucanas and mixed breed Easter Eggers. I used to raise chickens as a hobby, my Americana hen was the only one of them to lay green eggs. All of them got the same feed and foraged in the yard eating bugs and various plants. There was an effect on the clearness of the whites and the color of the yolks, the yolks having a darker orange color, possibly from pigments from their foraging.

Interestingly enough, it seems that the egg color gene is passed by the rooster rather than the hen, because none of the daughters of my Americana hen ever laid any green eggs. That, or the brown egg color gene is just more dominant.

Source: You made this up

The eggs depend on the breed of the chicken, not the nutrients themselves.