To me, **** kickers were regular leather work boots. Or say insulated rubber boots worn in the cold and snow and when things were deep (standalone, not worn over leather boots).
I don't recall calling regular buckle-up rain boots **** kickers. They are pert near that, so I am less certain about that.
Rubbers, with the soft rubber button fastener, might have been called rubbers or rain boots or boots. By brand name they were Tingleys, which I believe we called them some, but probably not a lot. I recall that the veterinarians wore them more than we did.
Probably most people still know what "it is getting pretty deep in here" means.