there is a cartoon about one old lady who swallowed a fly. in one moment the cat says: "And she had a frog on the sly" What does it mean?
From The Free Dictionary:
Idiom: on the sly
In a way intended to escape notice: (example) took extra payments on the sly.
Without knowing the context of the rest of the cartoon, this could mean either she possessed a frog without anyone noticing or she ate a frog without anyone noticing.
Assuming you are referring to the story by Simms Taback:
As an idiom, "on the sly" means furtively or without intending to be caught or seen. In the context of this presentation, the horse is accusing the old lady of not only eating the traditional farm-load of animals, but of also having eaten a frog. (A frog is not traditionally in the list of animals eaten by The Old Lady Who Swallowed a Fly.)