more than one vortex!
Okay, here's what I remeber from wing design 101:
with flaps extended, you have some of the vortcity shed from the outboard edge of the flap, and another one shed from the wingtip, as shown most excellently by the above pic.
Both of those are rotating in the same directions (clockwise / anticlockwise, depending on which wing)
So the upwards component of the vortex from the flap is superposed with the downwards component of the wintip vortex, thus reducing the overall vertical component of the airlfow in the interaction field.
With a clean wing at the same weight and airspeed you get the same lift, but the whole kick of the lift is off of the tip vortex, without the canellation effect.