I recently read A Man of Parts and Learning, Fara Dabhoiwala's London Review of Books article.
A fascinating account and aside from a poem Williams wrote in honour of a British governor of Jamaica, nothing we know about Williams is in his own voice. Our perception of him today largely comes through other people, notably the absentee plantation owner and colonial administrator Edward Long, who was a vocal advocate of slavery.
The painting is held in the collection of the V&A Museum in London - on the link is a detailed analysis and annotated 'tour' of the image.