Just a small note:
On a flex take-off Vmcg will still be Vmcg for TOGA, same for Vmca. Since TOGA can always be applied......... For a flex take-off all the TOGA requirements will still have to be met.
Vmcg/a can only be reduced with a de-rate. With de-rate I mean that the thrust-rating of the engine is physically reduced (done on some Boeings).