For family tree see William Mackenzie on Ancestry (subscription required)
William Mackenzie (1773–1819) was the younger son of Alexander Mackenzie, 9th of Fairburn, and Catherine Baillie (a daughter of William Baillie of Rosehall) - and so a nephew of the slave factor George Baillie and a cousin of Robert Sutherland, merchant in St Vincent.
He was in partnership as a slave factor in Demerara with James Craufurd Macleod of Geanies. This is confirmed by a reference to George Baillie being the uncle of the Mackenzie in this partnership [NRS GD46/17/21 f.237-240].
James Baillie Fraser of Reelig was indentured to John Bruce and William Mackenzie, merchants in St Vincent, on 19 Feb 1799 [Reelig papers?], before moving to Guyana.
William Mackenzie died in Florence leaving, among other legacies, £2000 to Margaret Lincoln of St Vincent £2000 and £5000, when he came of age, to his reputed son Alexander McKenzie at present at 71 Cornhill [LBS William Mackenzie of St Vincent].