As the question indicates, Jamaica Kincaid’s writing borrows heavily from her real life, or, as the questions puts it, “personal biographical events.”
Regarding her story “Biography of a Dress,” many of the details in the work relate to aspects of Kincaid’s real life. In the story, the narrator notes how, after dinner, her mom’s husband, who was not her biological father, would go for a walk. In real life, not only was Kincaid raised by her mom and her stepdad (her biological dad abandoned her), but she was remarkably close to her mom.
The close mother-daughter relationship in the story is evinced with the narrator states,
My mother not only took me with her everywhere she went, she carried me, sometimes in her arms, sometimes on her back; for this errand, she carried me in her arms; she did not complain, she never complained.
This excerpt shows that the narrator and her mom are basically inseparable. If the narrator is a burden on her mom, the mom doesn’t say so.
The intimate link between the mom and the daughter could reveal something about gender. As traditional gender norms tend to go, it’s the mom’s duty to care for and raise the child and to do so without protest.
As for sexual discrimination, think about the penultimate paragraph, in which the narrator’s photo is taken by Mr. Walker. After Mr. Walker tells the narrator that he admires the “plaid taffeta ribbon” in her hair, the narrator thinks “he perhaps wasn’t a man at all.” It’s not hard to identify stereotypical gay tropes in this scene. Mr. Walker’s interest in clothes seems to compromise his masculinity. In the story, clothes are perceived as a feminine domain. When Mr. Walker expresses admiration for the speaker’s style, the speaker becomes suspicious.
The speaker herself is subject to a type of gender discrimination as well. When her mom and her go back to their house on Dickenson Bay Street (a real-life street), people say how beautiful she is. This moment arguably plays into the idea that it’s permissible to comment on a female’s appearance even if she is a two-year-old child.