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I don't think galaxies are moving towards the cold spot. The CMB cold spot is located in the direction of the constellation Eridanus. Dark flow, on the other hand, is moving in the direction of Hydra and Centaurus.I don't see any particular reason that the flow can't just be caused by gravity from a giant supercluster of galaxies beyond the edge of the visible Universe. Seems to be a more conservative guess than invoking parallel universes or new physics.
It is generally agreed that the influence of gravity propergates at the speed of light, if the source of attraction was beyond the limit of the observable universe as regards electromagnetic radiation would the same thing not also apply to gravity ?.