Wikipedia has this:
A distinction is made between joint possession (Jason and Sue’s e-mails: the e-mails of both Jason and Sue), and separate possession (Jason’s and Sue’s e-mails: both the e-mails of Jason and the e-mails of Sue). Style guides differ only in how much detail they provide concerning these. Their consensus is that if possession is joint, only the last possessor has possessive inflection; in separate possession all the possessors have possessive inflection. If, however, any of the possessors is indicated by a pronoun, then for both joint and separate possession all of the possessors have possessive inflection (his and her e-mails; his, her, and Anthea’s e-mails; Jason’s and her e-mails; His and Sue’s e-mails; His and Sue’s wedding; His and Sue’s weddings).
More here: http://en.wikipedia.org/wiki/Apostrophe#Possessive_apostrophe
So in your example, unless they are writings that Giovanni and Walker co-wrote, you should use Nikki Giovanni's and Alice Walker's writings. Although I agree that it trips off the tongue better with just the second 's, and no doubt only the pedants in the audience would pick you up on it ;)