Parkinson was employed by Joseph Banks to travel with him on James Cook's first voyage to the Pacific in 1768. Parkinson made nearly a thousand drawings of plants and animals collected by Banks and Daniel Solander on the voyage. He had to work in difficult conditions, living and working in a small cabin surrounded by hundreds of specimens. In Tahiti he was plagued by swarms of flies which ate the paint as he worked. He died at sea on the way to Cape Town of dysentery contracted at Princes' Island off the western end of Java. Banks paid his outstanding salary to his brother.
Parkinson is commemorated in the common and scientific name of the Parkinson's PetrelProcellaria parkinsoni. The great Florilegium of his work was finally published in 1988 by Alecto Historical Editions in 35 volumes and has since been digitized by the Natural History Museum in London.