What conflict does Wylie introduce with the lines "down to the Puritan marrow of my bones/there's something in this richness that I️ hate"? How do the lines in the stanza develop his conflict?

This is internal conflict.

She's saying the Puritan part of her ancestry would hate the richness of the setting. Puritans were known for austerity and simplicity.

In most of the poem, she is describing a rich world where "peaches grow wild," "when April pours the colors of a shell Upon the hills." Toward the end of the poem, she shifts and describes this internal conflict. Here, she is saying that a part of her would hate the richness of this world.