Hello ludovico
I asked the exact same thing here at tech log some time ago and couldn't wrap my head around it, but it seems Brian Abraham has a really good point.
I was thinking that flap couldn't affect the vortex since flying an airplane in a given IAS has to produce the same amount of lift, and hence induced drag, whether it is configured with flaps or not. Here is where I guess I was wrong:
A vortex being dependent of the downwash angle from the airfoil to the direction of flight and the pressure differential between the upper- and lower side of the airfoil, is then dependent of the aspect ratio of the wing.
As we read during our studies that's why the gliders have long wings.
But.. lowering flaps shifts the centre of pressure laterally towards the area of the flaps due to the increased camber and downwash angle. When maintaining the same amount of total lift this means less pressure differential toward the wingtips, as if there was a higher aspect ratio.
Meaning smaller vortex when lowering flaps.
As said so many times in this thread.. this is just my theory. If I am corrected I see that as a chance of learning.
I hope this may have been of some help.