The conflict in "The Flowers" is that of a child's life of dreamy beauty and innocent happiness clashing with the cruel reality of racial hatred and its death message.
When Myop, (whose name suggests the descriptive adjective, myopic) starts out it seems to her that "the days had never been as beautiful as these." A happy, carefree girl, Myop strolls along, tapping the beat of a song on the fence with a stick:
She was ten, and nothing existed for her but her song.
But, this day she ventures farther than she usually goes as she gathers flowers and explores. One spot seems strange as the air is damp, and "the silence close and deep." So, Myop decides to head back to her house where it is peaceful; however,
[I]t was then she stepped smack into his eyes. Her heel became lodged in the broken ridge between brow and nose, and she reached down quickly, unafraid, to free herself. It was only when she saw his naked grin that she gave a little yelp of surprise.
Yet, she is still tempted to gather flowers. As she notices something around the root of a rose and she stoops to pick it, her innocence collides with the brutal reality of what has taken place in the spot where she has sought this pretty flower: Coiled around the stem of the rose is a rotted piece of a noose,
...a bit of shredding plowline, now blending benignly into the soil. Around an overhanging limb of a great spreading oak clung another piece. Frayed, rotted, bleached, and frazzled‐‐barely there‐‐but spinning restlessly in the breeze. Myop laid down her flowers.
Myop's dreamy gathering of flowers is terminated. She releases the flowers from her hands, laying them on the ground where a man has been lynched, a reality that looms in the still, dead air she breathes. "And the summer was over." Her innocence is lost.
The conflict in this story is that of racism with Myop's discovery of the remains of a lynching victim. The role of racist violence and the acceptance /approval from law enforcement form the main conflict.