What is a thorough way to clean my dish rack?
Bleach is your best bet.  Scrub it with a long-handled scrub brush and either liquid bleach or Ajax and water.  Let it soak a bit before rinsing it out.  Since it's stainless steel, the bleach won't do it any harm and will kill off any organics growing on it.

In my experience, the pink stuff is a mold, not flouride.