I believe that what you have is an early version of the rubberized "Battery Service Kits", that most of us are used to seeing. These kits were usually found in the Gas Station's/Garage's "Service Truck". In the kits, one would usually find: a small container of battery acid wrapped in hemp, a container of distilled water, one or more pairs of battery terminal pliers. In some kits one could/would find: a Hydrometer and a battery cell tester.... Of course a pair of jumper cables would be found in newer kits (push start was the norm back in the teens, 20s and 30s)
Not a lot of the metal kits survived,IMO. Rubber kits became more and more practical as they took the beatings from being in the tool box much better than steel....
Looking for Tide Water/ Tide Water-Associated/ Tidewater items