Why does young Marguerite make the choice to speak to Ms. Flowers?

Young Marguerite makes the choice to speak to Mrs. Flowers because she senses that the older woman is different from the other adults in her life. Mrs. Flowers never makes Marguerite feel like she's at fault for not wanting to talk. She accepts Marguerite for who she is and never belittles her for her fears.
For her part, Marguerite is fascinated by Mrs. Flowers. The older woman reminds Marguerite of "women in English novels who walked with their dogs" and "who sat in front of fireplaces, drinking tea and eating cookies." In other words, Mrs. Flowers is refined and sophisticated. Marguerite thinks that Mrs. Flowers is as "well-mannered and civilized as white folks in the movies and books." Despite her obvious education, Mrs. Flowers remains friendly and modest.
It is Mrs. Flowers who tells Marguerite that "language is man’s way of communication with other people and it is language alone which separates him from the lower animals." Additionally, during her visit with Mrs. Flowers, Marguerite is made to feel right at home. She enjoys cookies that Mrs. Flowers has baked just for her, and she revels in the thought that she will be able to bring some of those cookies home to share with her brother. Later, Mrs. Flowers reads to Marguerite from A Tale of Two Cities.
Although Marguerite has read the book herself, she is held spellbound by Mrs. Flowers' voice as she reads. Throughout her whole experience at Mrs. Flowers' home, Marguerite is made to feel like she is valued for who she is rather than who she is related to. This makes all the difference in how Marguerite responds to Mrs. Flowers. While the other adults in her life try to control Marguerite, Mrs. Flowers is more focused on communicating with her young friend.
Mrs. Flowers' unique perspective on life and her kindness to Marguerite inspires Marguerite to open up to her.