Green’s Dictionary of Slang

kit n.1

[SE kit, a small fiddle, esp. popular among dancing-masters; ult. ? Gk cithara]

a dancing-master.

[UK]New Canting Dict. n.p.: kit [...] a Dancing-Master.
[UK]Defoe Street Robberies Considered 32: Kit, Dancing-Master.
[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: Kit, a dancing master, so called from his kit, or cittern, (a small fiddle) which dancing masters always carry about with them.
[UK]Lex. Balatronicum [as cit. 1785].
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue [as cit. 1785].