That's a cool one Brian! So the Flow command works just by making a mapping from the base surface to the target surface. A point on the original object is mapped to the closest point on the base surface which gives a u,v value in the base surface's parameter space. Then that same normalized u,v value is evaluated on the target surface. So the result is dependent on the parameterization of both surfaces and does not have any special properties for preserving distances or angles or such things.

- Michael