The flow of momentum is a more precise concept than the
flow of water. Water (in many practical situations) is
very nearly conserved, but momentum (so far as I've heard)
is always strictly conserved.
The laws of conservation of momentum (along with energy,
charge, and various other things) are the heart and soul
of physics as it is understood today. These laws are
nothing more nor less than flow statements.
Flow can be explained in various ways. One particularly
grand way is in terms of the continuity of world lines.