Do I get a discount on the flexible fare Europe with the BahnCard?

Yes.

You receive a 25% discount with the BahnCard 25 or a 50% discount with the BahnCard 50 on the German part of the journey.
With a BahnCard 100 you receive a 100% discount on the German part of the journey (except France). Holders of a BahnCard 100 can take advantage of relations-dependent fixed prices for journeys on cross-border co-operation services to France.