J.B.
Just bake from scratch, which is quick, easy and cheap. Unless you add food coloring, sprinkles or colored chips/candy to a cookie, it has no dye in it (chocolate chip, peanut butter, sugar, oatmeal, etc.).
Brownies and blondies are easy to make from scratch and most mixes, even conventional brands such as Duncan Hines and Betty Crocker, don't add dyes to those.
Cake, cheesecake, pie, fruit desserts...the list of desserts without artificial colors is endless if you make them from scratch. Many yellow cake mixes and white frostings do have dyes in them so those are worth making from scratch. Most chocolate cake mix does not have color in it so you are safe to use mixes for those.
I wouldn't stress about this of go out of your way to buy expensive mixes. Just figure out what your kids like and make those without dye. I bake a lot and the only time I use food coloring at all is for adding color to icing. Other than that, it doesn't get used at all.