Neutrons don't flow like water. As others indicated, neutrons are subatomic particles, and in water they tend to scatter off other the nuclei, and considering that they are nearly the same mass a proton, they can lose nearly all their energy when colliding with a proton (if it the collision is straight on). So neutrons scatter off nuclei until they are absorbed by some nuclei.
A neutron will combine with a proton to form a deuteron, or a neutron will combine with O-16 to forum O-17 or O-17 to form O-18. If the neutron energy is high enough, it can even knock a proton out of a nucleus in an (n.p) reaction.
Neutrons as colliding particles collectively diffuse through water, and the diffusion is just a manifestion of the gradient of the concentration (population density) of neutrons in the water.