He engraved the statues of twelve apostles found in the church of St. John Lateran; and some of the plates for Gavin Hamilton's Schola Itálica including The Presentation in the Temple after Fra Bartolommeo.
He also engraved several of the plates for the Schola Italianate Pictures under the direction of Gavin Hamilton.
He was born in Rome, was employed by Gavin Hamilton to engrave some of the plates for his Schola Itálica; among these were the following: The Marriage of St. Catherine after Parmigianino; Meleager and Atalanta after Polidoro da Caravaggio; and Christ on the Mount of Olives after Giovanni Lanfranco.
Nonetheless Burns made many friends (his wife Jean Armour was born in Mauchline) and a lot of enemies whilst in Mauchline, many of whom are buried in the kirkyard: "Holy Wullie" Willie Fisher, the Reverend William "Daddy" Auld, John Richmond, "Clockie" Brown and notably Gavin Hamilton his best friend.
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However, many were also excavated in the 18th century by antiquities dealers such as Piranesi and Gavin Hamilton to sell to Grand Tourists and antiquarians such as Charles Towneley, and so are in major antiquities collections elsewhere in Europe and North America.
In 1763, Fitzpatrick was in Italy with the bibliophile, Topham Beauclerk; where he bought old-master paintings and commissioned paintings from Gavin Hamilton.
This was found in the pantanella of Hadrian's Villa at Tivoli by Gavin Hamilton in about 1769, and subsequently formed one of the Towneley Marbles collection bought by the museum.
Like many other artists in Rome he also acted as a dealer, working with Gavin Hamilton and Thomas Jenkins, and negotiating sales of antiquities to Frederick Hervey and John Campbell.