what is symbolic of the black flowers on the grave? How do they initiate the discussion and what is that discussion about?

Chillingworth has tried in vain to drain Dimmesdale's soul for his own purposes, and we get the clearest indication here, as Hester looks into his eyes and sees nothing but blackness and evil. Chillingworth is completely unable to forgive or pardon, and he senses with latent rage that events are beginning to happen independently of his purposes. Chillingworth, in his way, has sold his own soul to the devil, essentially disowning it, in the hopes of appropriating Dimmesdale’s vitality.

Hester sees this at once, but it is Chillingworth's final verdict that the "black flower" will continue to blossom that reveals his allegiance to evil. Chillingworth suggests that Hester's one act of adultery has spawned evil that will last forever, first through Pearl, and now in Chillingworth's relentless attempts to punish her and Dimmesdale. Hester accepts her role in the sin, but she cannot accept this perpetuity of evil. She actually will be vindicated upon Dimmesdale's confession, when the black flower will lose its power and slowly shrivel, giving way to new, unfettered life.