John Baillie died in Flanders in December 1743. Very little is known about him. He qualified as a physician and worked for a time at St George's Hospital, London, and with the English Army. He had written a play, The Married Coquette, which was published the year after his death by subscription to benefit his widow. In 1747, when Dodsley published Baillie's Essay on the Sublime, he also published a second edition of the play.
From The Continuum Encyclopedia of British Philosophy in Oxford Reference.