The problem with the statement that
You would expect minimum fuel flow to occur with minimum drag
is that it is based on a number of (often forgotten) simplifying assumptions.
One of these assumitons is that the fuel required to produce each unit of thrust is constant.
Vmd is the speed at which the thrust required is a minimum.
Vmd will also be the speed at which fuel consumption rate is a minimum
provided the fuel flow required to produce each unit of thrust is constant at all speeds.
The fuel flow required to produce each unit of thrust is the Thrust Specific Fuel Comsumption (TSFC). Unfortunately TSFC is not constant at all airspeeds.
To find the speed at which fuel flow will be minimum and endurance will be maximum we must take into account both the variation in drag and the variation in TSFC. In many cases this will give us a speed that is slightly higher than Vmd.