In this particular story, the noose represents a couple of things for Myop. To begin, Myop notices the first piece of the noose as she finds a pink flower. 

Very near where she'd stepped into the head was a wild pink rose. As she picked it to add to her bundle she noticed a raised mound, a ring, around the rose's root.

At this time, the noose doesn't represent much for Myop. It is seen as nothing more than a raised mound. As Myop investigates it a little more, the noose starts to take hold of her flower, almost as if to grasp the flower by the very thing that is holding it in that space. This is evident from Alice Walker's describing the noose as being a ring around the root of the flower. Again, Myop is still clinging to her innocence, too. She doesn't even realize what the noose is, because she is focused on the beauty of the flower. To this degree, the noose is the last piece of Myop's innocence. The story continues from here with Myop further investigating the noose.

It was the rotted remains of a noose, a bit of shredding plowline, now blending benignly into the soil.

To further view the noose as Myop's last bit of innocence, Alice Walker described the rotting noose oxymoronically, by stating that it benignly blends into the soil. In this sense, benign is used to signify gentle blending. Then, almost in a flash, the noose represents the destruction of innocence, a new and cold reality for Myop. 

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 sees this huge, encompassing tree, yet the tree is overshadowed by a barely there piece of rotting noose. The noose takes center stage, despite is being frazzled, spinning and rotting. The noose is all that Myop can process as she lays down her flowers. It ends her youthful frolics. The noose kills the sense of happiness and beauty that Myop had come to relish. After all, the dead body, the cracked teeth, the head that lay next to the body; none of those things affected Myop as that noose. The noose, however, changed how she viewed the world. 

What is the significance of the noose in "The Flowers" by Alice Walker?

It isn't just the discovery of a human skull that changes Myop. She is “unafraid” and only gives “a little yelp of surprise” having stepped on the skull.

It’s the noose that finally establishes the point that the skull belongs to the man that was lynched to death. As soon as Myop is able to relate “the rotted remains of the noose” with the “frayed, rotted, bleached, and frazzled” piece of a rope “around an overhanging limb of a great spreading oak” and the dead man, the noose acquires a deeper significance.

Now, the noose lies on the ground as a grim reminder of violence and hatred. It's like a lens through which Myop gets an actual glimpse of the world she belongs to. It carries her from her myopic and self-constructed pristine world, consisting only of nature in its beautiful and harmless forms, to the real world of ruthlessness and hatred.

In the story, the noose is a very important and powerful image as it’s through the noose that Myop unmasks the ugly yet true face of the world that surrounds her. It shakes Myop from within and leads her into a complete transformation that she wasn't prepared for. Now, she is out of the non-existent idyllic world and stands stupefied confronting the real world.