Made-up word, and ill-made. The verb stem "flow" is flu-, which gives (1) the noun flux- "flow" and (2) the participle fluent- "flowing" (-ent-, not -ant-, because flu- is second declension). (2) does not come from (1). From the participle ending -ent- comes the Latin abstract noun ending -entia. This, in French, not Latin, became -ence (as in influence etc.).
Antefluence is fine. I'm just finicky: I don't mind people madeupicking them, but if they appear to be Latin or Greek I like to see them properly done (and to have meanings of parts correctly explained, while we're at it); and I'm thinking of the puir wee kiddies who might take it for some venerable, battered word handed down from dictionary to dictionary and think it will impress others at the bar to bring it out in casual conversation, only to find their triumph ruined when some even more boring person challenges it and demands the pub dictionary.