''Kashlinsky speculates that the dark flow extends "all the way across the visible universe," or about 47 billion light-years, which would fit with the notion that the clusters are being pulled by matter that lies beyond known horizons''.
Some clarification here.
First, the "Visible Universe" is limited to ~13.7Gly. However the co-moving distance
is ~47Gly (radius).
The co-moving distance is the size NOW of the Visible Universe. The Cosmic Microwave Background defines the photon boundary, if you will, of our "bubble". Even though the current size/diameter of the Universe calculated (Standard Model) to be ~95Gly, we cannot "see" anything beyond 13.7Gly. Also, the Dark Flow region has been identified out to ~2.5Gly, NOT the whole visible universe. So there's a ways to go still.
Second, unless we have two "bubbles" colliding (this is just a comment to elude to a point, I don't believe any theory allows for this kind of multi-verse collision), anything "outside" our Visible Universe (i.e. BEFORE the Big Bang), is FOREVER outside our visible universe. HOWEVER, the idea of motion imparted to matter visible to us within our "bubble" IS possible. I think of it this way, and I think it was stated earlier,
every location within our bubble, has it's own bubble, and visible horizon. A conglomeration of mass could be visible to another far-away location, and therefore with the light cone for that observer. So that observer can be affected, and we see that obersver, so therefore we see the gravitational effects on that observer.
With that said, given we can only see ~1% of all the energy (normal mass that's visible), I think more data is needed to rule out the source of this large-scale motion is NOT in our observable Universe. There's another 26% of matter out there (25 times more than visible matter) that we can only indirectly "see" by weak lensing surveys. Unfortunately, the best one to-date (Hubble data) does not cover the Dark Flow region, but it does extend the matter / Dark Energy model out to ~13Gly! This is a beatiful bit of work and suggests that there is no reason to expect any regions of VERY large, locally contained mass concentrations. A similar survey in the Dark Flow region would be illuminating.
So the idea of matter motion ebb and flow being driven by regions outside our visible Universe is possible without breaking and laws of physics. Just as Ort Cloud or Kuiper Belt Objects can be pertubed by passer-by objects and change their orbits about the Sun, our visible Universe is much the same.