From Middle English ningkiling, nyngkiling, and then either:
; or
from inklen + -ing, -inge; inklen may be derived from inca, inke, from Old English inca, from Proto-Germanic *inkô, from Proto-Indo-European *h₁eng-, *yenǵ-. The English word would then be analysable as inkle + -ing.
Sense 3 (“desire, inclination”) may have been influenced by incline or French enclin.