One explanation for the flow would be the gravity of a huge concentration of matter, but this is very unlikely. Within the standard big bang picture, massive cosmic structures were “seeded” by random quantum fluctuations, so overall, matter should be spread evenly.
There could be an exotic explanation. Laura Mersini-Houghton of the University of North Carolina, Chapel Hill, thinks the flow is a sign of a neighbouring universe. If the tiny patch of vacuum that inflated to become our universe was quantum entangled with other pieces of vacuum - other universes - they could have exerted a force from beyond the present-day visible horizon (see “Nosey neighbours”)