Well, I've certainly never had my chickens peck at sound paint, and the vast majority of BYCers report the same... chickens will peck at *peeling* paint, but paint that is peeling needed to be redone ANYhow. (And done properly, i.e. with good surface preparation and then a thin coat of primer and then several *thin* coats of paint, otherwise it will peel prematurely)
I would not put it past a few unusual and/or bored chickens to peck sound paint but that is by far not what normally happens.
Painted surfaces are much, much easier to clean than unpainted; and outdoors (exposed to sun and weather) will last significantly longer.
FWIW, nowadays, regular ol' interior latex paint is (when dry) pretty entirely nontoxic, as are many exterior latex paints. Some exterior latex paints contain a small amount of mercury as a mildewcide, but it has to be listed as such on the label so you can recognize these and avoid them if you want. Of course, OLD (like, pre-1980) paint can have lead in it and is arguably not great for animals to be eating flakes of, but this has nothing to do with what you can/should/might paint your coop with NOWADAYS.
JME, good luck, have fun,
Pat