Green’s Dictionary of Slang

to toady, to curry favour.

1979		Sounds 28 April n.p.: A somewhat brown-tongued expression of gratitude for their come-back [KH].
1983		K. Hudson Dict. of Teenage Revolution 29: Brown tongue. An act of sycophancy, associated no doubt with the older-established ‘arse-licking’.
2001		D. Looser Boobslang [U. Canterbury D.Phil. thesis] 31/2: brown tongue it to curry favour with prison authorities in an attempt to get through one's sentence easily.