Frederick (Fred 'Diamond') Button was the son of James Clark Button and his wife Matilda Thurston and a brother of Edward ('Gold') Button*. The family came to Natal from England in 1854, but James died shortly after his arrival with the result that the family broke up. Frederick earned his nickname after achieving success on the diamond fields around Kimberley. In 1880 he was a clerk living in Durban. In October 1882 he married Esther Mary Tinline in Dover, England.
At a major symposium (then called a conversazione) of the just established Natural History Association of Natal, on 13 March 1868, Frederick was one of the exhibitors who showed a collection of birds. The association became defunct in 1871. In 1885 a movement arose to found the Durban Natural History Museum. Button was a member of the first museum committee appointed by the town council on 23 November 1885, and was elected its first honorary secretary and treasurer in February 1886. In this capacity he worked closely with J.S. Steel*, who was the moving spirit behind the new museum. He still held his two honorary positions on the committee by 1895.
In 1897 and 1898 Button was a member, appointed by the Natal government, of the committee whose object was to maintain the Natal Botanic Gardens in Durban. He resigned his seat on the committee in 1899.