The meaning of "Don't crash the ambulance" as a phrase, on its own and not viewed as part of the song, is pretty clear, surely. You have an accident or are otherwise injured - an ambulance is called to take you to hospital - you are in desperate need to get to hospital for treatement - you want that to be done speedily, so the ambulance is driven quite fast - but you don't want the ambulance to be impeded or stopped on the way - hence, "don't crash the ambulance". Don't stop those who are acting to help you from providing that help.
As for the song, I only really know MK's songs from their being performed in concert and, though my memory may be at fault, I can't recall him performing "Don't crash the ambulance" at any concert I've attended. If he has, it has passed me by.