As Golf-Sierra has said. Minimum fuel flow is exactly that, its the point where the aircraft is flying above the stall speed but as slow as possible with the minumum fuel entering the engines.
Think of at the point of minimum drag. Say the aircraft is burning 1000kg/hr to maintain say 250kts.
Now if everything was linear and drag wasn't involved you could say at 500kg/hr you would be flying at 125kts. Obviously this isn't the case, but with the extra drag at 500kg/hr you would maybe be flying at 100kts. As long as this speed is above the stall speed then your a happy chappy.
Basically the extra drag will cause you to lose some airspeed but you can still get a lower fuel consumption than flying at the minimum drag state.
After all the whole reason for minimum fuel flow, is exactly that. You want to burn as little as possible to stay in the air as long as possible, you are not looking to get anywhere fast, and so are not concerned about the increase in drag.
Its probably clearer in my head that what i've tried to describe but hope it helps.