The white feathering is making me think without seeing the legs that this is most likely a white rock or a leghorn. White Rock will lay brown eggs and leghorn will lay white eggs.
The chick in the pic looks to be between one and two weeks old going off the wing development. As for the rainbow layers.... Some places sell the Easter Egger chicks as "rainbow layers" meaning you could get white, green, or brown eggs. Other places sell a variety pack of chicks as "rainbow...