This ad appeared in the October 1806 La Belle Assemblee. He also advertised in his own booklet A Domestic Treatise on the Diseases of Horses and Dogs (1803):
A length review (we have only excerpted the first few paragraphs) of another of “Professor” Blaine’s work appears in The Monthly Review, Or, Literary Journal (1804).
We found several other books by Mr. Blaine as well as reviews into the years, where he is later referred to as a veterinary surgeon.
Mr. Delabere Pritchett Blaine even has a brief wikipedia entry that shares his clinic/kennel was in Wells Street in London, and that he struck up a partnership with William Youatt beginning in 1812 until 1824 when Youatt took over the business.