The standard interpretation of this is that the blackbird might be a shape-shifting female creature known as a "jablesse" or "diablesse" (from French "she-devil", the feminine version of the usual "diable" meaning "devil"). Wikipedia mentions her as "a character in Caribbean folklore" but does not mention the shape-shifting aspect and how she might be seen in the form of a bird. However, various other commentators on Kincaid's work and "Girl" specifically have noted this connection.
Firstly, just to set the scene, Kincaid has indicated in interviews that "Girl" is based on the kind of advice she received as a girl growing up in Antigua. So we can assume that the setting is Antigua or somewhere culturally similar. The mother in "Girl" is influenced by both Christianity and Obeah, a Caribbean tradition which draws upon West African roots.
Commentators on Kincaid's "Girl" have generally interpreted the "blackbird" line as follows:
Accompanying training in preparing local food is training in folk beliefs. The reference to these suggest their mundane quality: the power of nature to do harm is taken for granted. The blackbird might be a jablesse, a shape-changing female spirit whom one does not want to offend. The fish can invoke a curse. Thus, there is a world behind the world of public appearance and performance, one which has its own authority and its own rituals.
-- Keith E. Byerman, "Anger in a Small Place: Jamaica Kincaid's Cultural Critique of Antigua", College Literature 22(1), Third World Women's Inscriptions (1995), pp. 91-102 (bold emphasis mine)
Because objects may conceal spirits, the mother warns about the blackbird being something other than it appears
The blackbird might be a "jablesse" (La diablesse, "she devil").
a shape-changing spirit that often takes the form of a beautiful, deceptive, and deadly woman.
The jablesse lures men with her beauty but then isolates and devours them. (Note how the folklore reflects attitudes about female gender roles)
-- Class Notes: "Girl" by Jamaica Kincaid, from the blog of Christiane Alcantara, an academic specialising in Caribbean literature