An unknown force is pulling the Milky Way towards it at 14M mph

Just to make it more meaningful, that's 6.258e6 m/s (Earth escape velocity at the surface is 11.2 m/s, Earth runs around the Sun at about 30 m/s, Sun runs around the Milky Way at about 200e3 m/s).

It's not because B moves toward A at speed V, that B is attracted by A. Attraction should be expressed as force (given in N), or, given the mass of the attracted object, as an acceleration (given in m/s²). The speed of the attracted object is irrelevant. In general in the universe, attractions are approximately perpendicular to the speed of the attracted object! (orbits).

Right now, Earth is moving toward Sagitarius at the speed of 30 m/s. Does it mean that Earth is attracted by a big unknown force pulling it toward Sagitarius at 30 m/s? No! This is bullshit. Earth is attracted by the Sun with a force of 3.5e+22 N, which gives an acceleration of 0.006 m/s², both of which are perpendicular to the speed of the Earth with respect to the Sun!

Adrian Berry didn't report any observation that the galaxies are accelerated in the same direction they're moving to.

The "Great Attractor", it's called, is quite interesting. Though this article doesn't delve much into it, there's more information about it on wikipedia. https://en.wikipedia.org/wiki/Great_Attractor

Advice: Note the date before starting a mathematical discussion on whether this is possible :-)