The section of the novel that you want to look at is Chapter Fifteen, which introduces Mrs. Flowers to us and also narrates the first visit that Maya paid to Mrs. Flowers, and the impact it had upon her character. We are never told directly why it is that Mrs. Flowers invited Maya back to her house, and the author herself tells us that she never thought about it at that stage in her life. Note what she tells us:
Childhood's logic never asks to be proved (all conclusions are absolute). I didn't question why Mrs. Flowers had singled me out for attention, nor did it occur to me that Momma might have asked her to give me a little talking to. All I cared about was that she had made tea cookies for me and read to me from her favourite book. It was enough to prove that she liked me.
From this quote we can perhaps infer that it was Maya's "Momma" who had asked Mrs. Flowers to have a chat with Maya. The author makes it clear that following her abuse she was sinking into some kind of deep depression and low self-esteem plagued her. Momma would clearly have noticed that Maya was suffering, and, given Mrs. Flowers' status in the community as the "aristocrat" of the community, presumably she felt that Mrs. Flowers would be able to help Maya.
Also, from what we know of Mrs. Flowers, we can tell that she is a caring individual who would likewise have wanted to help Maya get over the horrendous experience she had suffered. As a black woman who manages to be proud of her identity, she would want to help somebody like Maya to attain that same level of pride in herself.