Green’s Dictionary of Slang

a mugger or thief, esp. of watches, working in a team; one man grabs the victim from behind, while the flimper steals his watch.

1862		Morn. Post 18 Dec. 3/3: Let your flimpers and fakers match if they can / The deeds of my bold High-toby-man!
1891		F.W. Carew Autobiog. of a Gipsey 409: Square indeed! I’ll square the chatty flymps [...] I’ll precious quick make ’em granny who’s omee here.
1949		Monteleone Criminal Sl. (rev. edn) 87: flimp [...] one who robs persons.