First, if you are flying straight and level then min drag = min thrust (always).
The next thing to consider is the relationship between fuel flow and thrust.
If the thermal efficiency of the engine were constant (which it probably isnt) then fuel flow would be proportional to power developed. (with a jet, of course it is difficult to measure power developed anyway)
The relationship between power developed and thrust depends on the propulsive efficiency of the engine/ fan/ prop etc..
In the case of a "theoretical" jet engine which had no conversion losses due to fans, turbines etc, (ie a pure actuator disk) the propulsive efficiency increases linearly with speed and is given by
efficiency = 2*U/(V+U)
where U=TAS and V=speed of the efflux relative to the aircraft. This of course is the reason why big fan engines are more efficient than turbojets.
In this theoretical case, thrust is proportional to fuel flow and the two speeds are the same.
In real engines, of course things are not so neat. With a prop in particular, propulsive efficiency does not obey the above equation, and min ff speed is likely to be lower than min drag.