Red mites can live virtually anywhere as they are so small. As a rule they don't live on the birds but hide in crevices and cracks (even the irregularities in concrete) and come out at night to suck blood from the birds.
If your chooks sleep on proper perches perhaps you can make them so that they are easily removed/put back with pins and keep a spare set. They can be cleaned and put out in the sun and changed over every week. A layer of vaseline (or grease) at both ends of each perch will slow the little blighters down and make it difficult for them to reach the fowls.