Almost nothing is known about this artist, but he may very well be the John MacKay (sometimes spelled M'Kay) included in the New York City directory from 1790 to 1812. Although he is sometimes listed as a glazier as well as a painter, the combination would not have been unusual. Christin Skeeles Schloss notes a John M'Kay listed as "printer" in New York intermittently between 1813 and 1823.
In addition to the National Gallery's portrait of Catherine Brower (1956.13.5), two other signed works by this artist have been discovered to date, Hannah Bush and John Bush. The three portraits share certain characteristics: all are dated 1791, depict New York residents, and display a peculiarly bright palette with prominent reds and blues. [This is an edited version of the artist's biography published in the NGA Systematic Catalogue]
Dresser, Louisa. "Portraits Owned by the American Antiquarian Society." Antiques 96 (November 1969): 722-723.
Schloss 1972, 41.
Chotner, Deborah, with contributions by Julie Aronson, Sarah D. Cash, and Laurie Weitzenkorn. American Naive Paintings. The Collections of the National Gallery of Art Systematic Catalogue. Washington, D.C., 1992: 247.