How did A Journal of the Plague Year relate to Defoes life?

Sadly, not really. Defoe was only 5 in 1655 when the story is set. It is suggested that the very realistic and detailed text was a fictionalised account of the experiences of Defoe's uncle, Henry Foe. We can conclude that the stories of Defoe's uncle may have been part of the family history, tradition and storytelling and that Defoe 'grew up' with the knowledge of the terrible events of that time, but not that he himself experienced them so directly.