There are a lot of factors contributing to effect of flaps on Vmca. On some airplanes it will increase others it will decrease. Let me try and give some examples of some of the factors:
1. Type of flaps: Split flaps for example, will generally have a lowering effect on Vmca (BilliBob, I know Vmca is always the same, but for the sake of the argument blah blah blah) if deployed as they primarily produce drag, and almost zero lift, therefore they will have a stabilizing factor. If you have flaps that generates high amount of lift you might experience increased roll towards the dead engine due to slipstream. On some airplanes you might experience selecting flaps 20-25 will add 1 or 2 knots to the Vmca, but going for full flaps, it might decrease a couple knots as the last step of flaps is mainly drag on many flap types.
2. Position of flaps: If your engines are located on the tail, there won't be much of a slipstream over the flaps and therefore lower Vmca with flaps out. So to put 1 and 2 together, you will see that amount of power, position and type of flaps are some factors.
3. Counter or Co-rotating engines: Most types of flaps enables you to fly at a lower angle of attack at a given airspeed - hence you can say, that p-factor or asymmetric blade effect will decrerase with flaps down. With co-rotating propellers, that will be an advantage (lower Vmca because thrustline moves closer to the center), but with counter-rotating propellers it will be a disadvantage, as there is no critical engine, and with a lower AOA the thrustline will move AWAY from the center.
The conclusion is that the effect of flaps has many variables. In any case it will not change the Vmca drastically on most airplanes. Only very few POH's state Vmca with and without flaps. Sometimes it is stated in the Type certificate data sheet. I have copied this from the type certificate data sheet of a BAE HS748:
Airspeed limits: Vmo (Maximum Operating)
From sea level to 15000 feet 225 kts.
Above 15000 feet 215 kts.
Va (Maneuvering) 155 kts.
Vfe (Flap Speeds)
Flap deflection 7 1/2° 180 kts.
Flap deflection 15° 180 kts.
Flap deflection 22 1/2° 140 kts.
Flap deflection 27 1/2° 120 kts.
Vlo (Landing Gear Operation)
Operation 160 kts.
Extended 160 kts.
Vllo (Landing Light Operation)
Operation 140 kts.
Extended 140 kts.
Vmc (Minimum Control Speed)
82 kts. (Flaps 0 < 22 ½ O)
81 kts. (Flaps = or >22 1/2°)
Notice only 1 knot difference.
I hope this answers your question, otherwise I suggest you ask the CI at your flying school, as I am sure he will know
