Ever since I was trained in soldering/desoldering techniques back in the day, I've always preferred to have fluxes within easy reach when I'm working on a board. I don't even think about it anymore, in fact it never occurred to me NOT to flux my wick.
"flux my wick"... that's what she said.
I use wick and pump, depending on the solder amount to remove. Typically I'll pump off the bulk of it and use the wick for the fine cleaning. Good wick has a high affinity to solder, and any hot solder will seek it out, preferring the wick over whatever it was on originally. Works like a charm.