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.
Heh, but how many wee ones are actually on Wordie particularly?
Then again, if I'd found this site when I was eight, I'm sure I'd have been totally enthused with it then as much as now. A geek is me, was me, and always will be. ^^;
Edit: And... I think you might likely be speaking of slightly older kiddy-esque creatures. I'm rather bad at picking up on some of these things sometimes. Especially since I don't expect to see an eight-year-old in a pub generally. xD
Like me? *smiles innocently* Stop luring me into pubs, Wordies! You are corrupting meeeeee!!
I'm fairly sure the pub down the street from my Mum's house (in my hometown) would have a dictionary. Because the publican is one of those who would be likely to whip out Latin words to impress others.