The OP asked for suggestions for flat shoes as she's probably going to be standing around at networking events. She has said standing around in heels is a pain. And it is - heels that are fine to walk in can quickly become painful when you're standing still on one spot.
I don't agree that flats are wrong but OP wants some sort of heel too.
I think a low heeled wedge would go with the dress and it's the most comfortable option for standing still on one spot. Standing still in heels concentrates all your weight on the ball of the foot - a wedge distributes it evenly.
Low heeled wedge