Dust baths are supposed to suffocate mites. If you want to add extra stuff, add diatomaceous dirt (a chemical, so you might not like it), lavender, or some other herbs. Ashes from fires are also good for them.
Food grade DE is not chemical.
DE has been proven to be totally ineffective for dealing with mites. It is also a lung irritant. I would skip it in the dust bath. Wood ash is helpful
This is not right. Its just not scientifically researched! I have 8 years of experience with DE and I dare to say it helped me / my chickens a lot.
The food grade DE is not irritating when mixed with sand or earth. Only when it largely pure. I use it as a paint (stir with water) to cover all parts of the coop and especially the roost and joints with the wet DE- After drying it sticks to to walls. Reapply when it disappears. Put a layer of sand with DE in the nest boxes under the bedding and clean out the bedding weekly if you have chicks (nest sleepers).
Imo DE can help a lot to prevent feather lice, scaly legs or a red mite infestation but you always need to monitor to be sure things are okay. My chickens never had scaly leg mites ar feather lice using DE.
For red mite you need more than just add a little DE in the dust bath. Furthermore to prevent an infestation that gets out of control you need to check / monitor weekly. I use rolls of biscuit paper (corrugated) to monitor and catch red mites.
Nest sleepers and not cleaning out weekly/not reapplying probably caused my last (minor) red mite infestation. I was glad I monitored the roosts, were I found a few mires. But this time it already spread in the nest boxes.
I concurred the red mite with cleaning , apllying lots of DE and adding special supplements to the water and feed. Here they sell Finecto+ supplements to make the chickens blood disgusting for mites. The chicks and chickens didn’t get any respiratory problems because from the DE the way I used it.
In my country chemicals like Permethrin are not allowed on animals kept for food (eggs and meat). And the poisons don’t work sometimes because the red mites build up resistance.
I have no experiences with the northern fowl mites.
Getting red mite is a problem with healthy chickens too. The blood suckers weaken your chickens. And after that chickens become unhealthy. Not the other way aound.
If you give balanced food you can feed chickens other things than commercial chicken or layer feed. It’s mainly the fatty/low protein treats you should give not too much. Free rangers in a lush environment can find lots of the food they need by themselves.
@Perris wrote an excellent article about feed if you are interested in feeding your chickens self made feed.