Some hatcheries offer "Rainbow Rangers" I've heard these are Freedom rangers with a name change. These are a broiler type bird. Meyer offers a Rainbow Pullet Assortment. These are just a mix of different egg colors. Good luck. Blaine
I was reading on a website (can't remember where) that they were working on a rainbow chicken breed that all the chickens in that breed came in different colors (I guess like the Icelandics and Flower hens).
I found that Mt Healthy offers "dixie rainbow" chicks. They are brown egg layers but the adults are of mixed colors. Some time ago I read an ad that stated they lay different shades of eggs. I can't find it now nor can I remember but it was a hatchery.
From the ones I've seen, the "rainbow" refers to the color of the chickens, not the eggs. They might or might not throw in a few Marans or Welsummers for dark eggs or EE's for green or blue eggs, but the ones I have seen don't guarantee that. They just throw a mix of different breeds, colors, and patterns of whatever chicks they hatch.
They never know exactly how the hatch will go. It is a good marketing tool for them to get rid of the excess chicks they hatch. They normally hatch popular breeds, colors, and patterns, so most people are happy with what they get.