Green’s Dictionary of Slang

gums n.2

also gummers
[elastic gum, India rubber]

(US) rubber-soled shoes.

[US]Night Side of N.Y. 119: One ‘young sport’ [...] rejoiced in a pair of odd-mated rubber over-shoes, about the dimension of snow-shoes. They saluted him as ‘Gums’.
[US]Number 1500 Life In Sing Sing 249: Gummers. soft or rubber shoes worn by sneak-thieves.
[US]Monteleone Criminal Sl. (rev. edn).