Vaseline can be used effectively but it only kills adult mites by suffocating them. This leaves the mite eggs still living.
If your chicks do have mites ( I really hope they don't) then you will have to clean out the coop. Mites will live in the cracks of wood, like the crate and coop/perches...
To answer your question it really depends on whether the chicks were hatched in an incubator or with a broody hen in a coop at the farm. If they were incubated then it is very unlikely that your chicks have mites (unless they get them your current coop). If they were hatched in a wooden coop at...