The best way to kill red mites or any mites on chickens is to sprinkle the chickens with some Pestene which is a sulphur and rotenone powder.
The Pestene powder will dehydrate the red mites and any other type of chicken mites.
You should sprinkle the Prestene around the chicken coop as well to help kill off red mites as well as other chicken mites.
The Prestene powder is also harmless to the chickens but will kill the mites.
If you notice mites around the chicken coop you can also kill the mites around the chicken coops by pouring boiling water on them.