Green’s Dictionary of Slang

(US Und.) a cigar or cigarette end.

1922		Appleton Post-Crescent (WI) 2 May 9/4: Flapper Dictionary dincher – A half smoked cigaret.
1925		G.H. Mullin Adventures of a Scholar Tramp 47: He may be smoking a dintch.
1926		Maines & Grant Wise-crack Dict. 14/1: Slip the dincher – Give one a half-smoked cigarette.
1950		Goldin et al. DAUL 58/2: Dincher. A cigarette butt, usually one that has been smoked more than once, a clincher; a snipe.