Food coloring should be safe if you do not get too crazy with how much you give them. A few drops is fine, a bottle may be too much. To dye their food, I think it would be best if you mixed the food coloring with water, then added that to their food. Mix it well. If the chickens are used to getting dry food, ask an adult in your family to help you dry it by spreading it on cookie sheets and putting it in the oven at a low temperature until it is dry. If the chickens are used to getting wet food, you can just feed it to them that way.

Birds do not have much of a sense of taste, but they have very good eyesight. Do you think they will avoid the colored food?

Good luck with your experiment.
Thanks for asking,