Minkowski says time is a coordinate, which is quite a different thing from a 'variable'. Coordinate axes do not 'flow'. If one was born on a smoothly-moving train which never accelerated or decelerated, and grew up on that train, one would 'conclude' that the 'x-axis' of space flows. No evidence to the contrary; just look out the window!
--Boris
Note that I said that time was "variable" and not "a variable." By this I meant that time is not independant of space (i.e. cannot be measured in absolute terms, regardless of motion and/or position). I can see where the term might have expressed a connotation I did not intend; sorry about that!
As for time "flow," imagine growing up on a spaceship which constantly accelerated from zero to lightspeed and back. Time would certainly "flow" (or ripple) if measured under those conditions, as it would move faster or slower depending on the velocity of your ship at any moment. Besides, time does "flow" normally, as a dropped ball shows the direct flow of time (the ball doesn't hover or reverse directions)...