"Everyday Use" was written and takes place in present day, 1973. The first page of the story makes reference to Johnny Carson, who hosted The Tonight Show from 1962-1992. The early 1970s were also the height of the Black Nationalism movement in which several high-profile African-Americans were changing their "slave names" to Muslim ones (e.g. Lew Alcindor become Karim Abdul-Jabar), following the likes of Cassius Clay (Muhammad Ali) and Malcolm Little (Malcolm X, or El-Hajj Malik El-Shabazz).
Mrs. Johnson, the narrator, says that she quit school in "1927" after finishing the 2nd grade. That would make her about 53 years-old, having been born around 1920 (date not mentioned). Dee, the older daughter, is in college, around 20 years old, probably born in 1940 or so. Incidentally, Alice Walker was born in 1944, so she's about the same age as Dee or Maggie, who is a few years younger than Dee.
Mrs. Johnson also mentions "Grandma Dee," who would have been about 20-25 years older than her, probably born around the turn of the century, 1900 or so. After that "Big Dee" is mentioned, who would have been born about 20-25 years prior to Grandma Dee, around 1880 or so, during the Reconstruction Era of the South. She would have been the first generation of freed slave.
So, we have four generations of women in the story, dating almost 100 years, from 1880 to 1973. All women were born in the Jim Crow South, which was segregated until only a few years before the story took place (1964), so only Dee and Maggie would have gone to de-segregated schools and reaped the benefits of the Civil Rights Era.