Does water flow down a drain in a specific direction on the equator?

It can and does flow either direction. It is a common misconception that water drainage down a sink or toilet is governed by the Coriolis Force, but in reality it is not since it takes about 6 hours of motion by a fluid for the Coriolis Force to have an effect. I have been on both sides of the Equator and have witnessed drainage in both directions in both hemispheres.