Middle English slinken, from Old English slincan "to creep, crawl" (of reptiles), from Proto-Germanic *slinkan (source also of Old High German slihhan, German schleichen "slink, crawl, sneak, move slowly," Swedish slinka "to glide," Dutch slinken "to shrink, shrivel"), related to the source of sling (v.)).
Of persons or other animals, "steal or move quietly" (frequently with off or away), attested from late 14c. Related: Slinked; slinker; slinking. As a noun, "a slinking fellow," by 1824.