In my experience flat spins usually occur at low speeds as you attempt to drop the wing opposite the direction of engine torque. Continuing to do so will cause a flat spin and the only way to counter the torque is to slow the engine.
Rapidly countering to the other side (attempting to drop the opposite wing) at full power near stall speed usually results in a snap-roll with the flat spin recovery being preferable to a snap-roll recovery.
I also found this little tidbit at
http://www.av8n.com/how/htm/spins.htmlRetarding the throttle is a moderately good idea for a couple of reasons. For one thing (especially if you have a fixed-pitch prop) it keeps the engine from overspeeding during the later stages of the spin recovery. More importantly, gyroscopic precession of the rotating engine and propeller can hold the nose up, flattening the spin and interfering with the recovery (depending on the direction of spin).
Propwash might increase the effectiveness of the horizontal tail and therefore assist in the spin recovery, but (especially in a flat spin) the propwash could be blown somewhere else by the abnormal airflow — so you may not be able to count on this.