[1] Fleming was born in Glasgow on 11 March 1833, and when still young moved with his father to Manchester, where both of them worked as farriers for veterinary surgeon.

He took medals and prizes, and in 1855 obtained the certificate of the Highland and Agricultural Society of Scotland, at that time a recognised veterinary diploma.

In 1860, he volunteered for the Second Opium War, and was present at the Third Battle of Taku Forts and the surrender of Beijing, receiving for his services a medal with two clasps.

In 1866, he obtained the diploma of the Royal College of Veterinary Surgeons, and in 1867, he served with the army in Syria and Egypt.

[2] Fleming became a vice-president of the Royal College of Veterinary Surgeons in 1867, a year after his admission, and a member of council in 1868.

[4] It was republished as Vivisection: A Prize Essay in 1871 by the Woman's branch of the Pennsylvania Society for the Prevention of Cruelty to Animals.

His published works included:[2] He translated from the French Auguste Chauveau's Comparative Anatomy of the Domesticated Animals (1873; 2nd edit.