She grew up as pop royalty, embodied mid-’60s glamour, romanced Elvis onscreen, and made the history books with “These Boots are Made for Walking.” All things considered, Nancy Sinatra’s career was one for the ages.

After a few false starts on her father Frank Sinatra’s Reprise label, Nancy was teamed in 1965 with the maverick writer/producer Lee Hazlewood. The first result was “These Boots are Made for Walkin',” still...