Heinrich Kling was a medically trained missionary of the Rhenish Missionary Society. He was ordained in August 1893. Later that year he came to South Africa and in December was stationed as assistant minister at the mission station at Steinkopf, Namaqualand. In 1898 he was transferred to the mission at Saron, near Porterville in the Western Cape, but found it difficult to function effectively as both a missionary and administrator of the Rhenish institute. He was transferred back to Steinkopf in 1907. There he married Elisabeth Dischereit, with whom he had two daughters. He had a good knowledge of local herbs, which he employed for medicinal purposes. His other interests included education, geological prospecting, ethnology, and agriculture.
During 1908 Kling presented many mineral specimens from the neighbourhood of Steinkopf to the Albany Museum, Grahamstown, including some rare copper ores. More minerals followed the next year, including a sample of agalmatolite (better known as pagodite), a soft silicate rock of which the San made their smoking pipes. In 1910 he and Mr. W.E. Griffin presented a fine group of minerals from Namaqualand to the South African Museum, Cape Town, including some large crystals of corundum and masses of native copper. Kling also donated some native ornaments (1909) and three San pots (1911) to the Albany Museum.
In 1912 Kling sold a Khoe skeleton to the Albany Museum. The museum's collections also include a male San skeleton sold or donated by him. Around the same time he provided the South African Museum in Cape Town with the skeletons of a male and female San and a male Khoe. All these skeletons were of people that he had known when alive and about whom he was able to provide the museums with personal details.
Kling was interred at Pietermaritzburg as an enemy subject during World War I (1914-1918), but returned to Steinkopf in 1918. Two years later he suggested that the Richtersveld mining district be opened up to relieve the distress of the people of Namaqualand. He retired in 1919 owing to poor health and after a brief stay at Tulbagh settled at Wolseley in the Western Cape. A few years later he published a pamphlet, Die sieketrooster... (The sick-comforter...; Cape Town, 1923), a short treatise on home medicine adapted on the basis of the medicinal plants of South Africa. He had also studied the culture of the people among whom he had worked in Namaqualand and regularly published his observations in Die Kerkbode. A number of these articles formed the basis for a book, Onder die kinders van Cham... (Among the children of Cham, Cape Town, 1932), which also included articles on the mission pioneers of Namibia and elsewhere.
In May 1935 Kling left South Africa to visit Germany. During the voyage he sustained accidental burns and died a few days later.