Baillie went to London at age of 18 to study law, but liked art more. Shortly after getting to London, he joined the army. He served at the Battle of Culloden the Battle of Minden and retired with the rank of Captain. Baillie was later made the Commissioner of Stamps, which he was until 1795.
While he continued as an artist, what he is most famous for was his skill repairing and printing etching plates. He worked on plates by many artists, including Gerard Dou, Nicolas Poussin, and most notably Rembrandt. Apparently he got a number of Rembrandt's worn-out plates. The three best known:
- The Goldweigher: He did a really fine job on this. The prints from it are at least as good as those done personally by Rembrandt.
- The Hundred Guilder Print (Christ Preaching): He changed it in a rather bad way. He then cut it up, and sold the pieces separately.
- The Three Trees: The lower portion of this had been destroyed. Baillie redid that part of the plate by copying an old print. It is not bad, but does not have the feeling that was in the original Rembrandt.
A book of prints, after the above artists, was published in 1792, in two volumes, with subsequent editions.