Parkinson was born in Edinburgh; his parents were the Edinburgh brewer Joel Parkinson, a Quaker, and his wife Elizabeth.[4] His birth year is usually given as c. 1745, but is somewhat suspect as his mother was born c. 1700.[5] He had a brother, Stanfield, and a sister, whose name was Britannia.[6][7] The parents were members of the Edinburgh meeting of Quakers; John Fothergill was another member.[7] Parkinson's father died in 1749, leaving the family in financial difficulties.[5] Parkinson became apprentice of a woollen draper. According to his brother, he took "a particular delight in drawing flowers, fruits and other objects of natural history", becoming "so great a proficient in that stile of painting, as to attract the notice of the most celebrated botanists."[6][8] While no direct evidence exists that Parkinson received formal training in art, he has been connected to William Delacour, who taught drawing and design at the Trustees' Academy, and may have been influenced by other Edinburgh artists.[9][10]