In this quip, the term fairy is being used to imply homosexuality. "Fairy" is a somewhat archaic term for homosexuality that today would be considered offensive.
Nels Anderson in The Hobo (1923) said that “Fairies or Fags are men or boys who exploit sex for profit.” The word fairy appeared in the 1870s, and was universally understood by the 1890s.
(From Rictor Norton's "A History of the Word 'Gay' and Other Queerwords")
The joke comes from Frank's use of fairy godmother to mean the fairy tale character, a woman with magical powers who brings good fortune to someone (as in Cinderella), and Dean using the term fairy to connote homosexuality. Dean is saying "I have an uncle that we suspect might be gay, so we watch him closely." The "keep a close eye on" also suggests that homosexuality is something to worry about or police, so the joke reinforces homophobic norms (not at all surprising given the context).