Mulch? I get the free county shredded yard waste "mulch" that is brown. Ask them for the undyed material cause the chickens eat it. It may also have rot retardants that may have adverse reactions. Get the natural stuff.
I will dump a 50# Dog Food bag of this stuff out and the chickens will spread it ALL over. They love scratching through and eating something. The starting to compost bits are more interesting than the just shredded tree pieces. Stuff works great to absorb poop and smells. It rained and the ground is water logged at present. If left in a pile, the pill bugs accumulate. Bonus feed.
I vote for the undyed, untreated, natural wood bits.