The strongest vortices are produced by heavy aircraft, flying slowly, with wing flaps extended
Nope. Wiki got it wrong, clean is the answer. Lowering flap biases the production of lift towards the root (large camber change and greatly increased angle of attack because of the flap)
Quite right about the induced drag however. Induced drag on an airfoil is inversely proportional to the square of the airspeed and is directly related to the amount of induced downwash at the trailing edge of the wing. As the angle of attack is increased (because you're going slower) the induced downwash is increased.
Vortices don't only flow from the end of lowered flap, or the wing tips, but exist along the entire length of the trailing edge of a lift producing airfoil. They can be seen at time also from the tips of the horizontal stabiliser, and tip of the vertical stabiliser on aircraft doing asymetric work.