leo,
when we 'flex' we end up with a whole new higher set of speeds.
i personally like to think of it as a 'inverse' of improved v speeds (hope you are familar with improved v speeds) i.e. for a fixed ambient condition and runway length, you use 'flex' because you have too much thrust. when you reduced your thrust, you need to increased your v speeds to 'compensate' for the 'lost' of performance.
had you start off with insufficient thrust, then similarly you could achieve a successful takeoff by increasing the v speeds. obviously, the runway need to be sufficiently long.
i know it's a crude way of describing it but i hope it helps...
SR