The name was very popular until the 15th century in England, usually in the vernacular form Maud. Both forms were revived by the 19th century. This name appears in the popular Australian folk song Waltzing Matilda, written in 1895.
As an American name for girls, Kinsley was very rare before 1990. It has steadily grown in popularity since then, perhaps inspired by similar-sounding names such as Kinsey and Ainsley (both of which it has surpassed).