We know he had three paintings exhibited at the Chicago Columbian Exposition in 1893, and that Anthony Ludovici in The New Age (13:20:577) put him among a small group of Dutch painters who “possess good and interesting qualities” but were not worthy of the designation “master.”
The following information is from an article by Gerharda Hermina Marius, translated by Alexander Teixeira de Mattos on Wikisource:
Johannes Christiaan Karel Klinkenberg, born at the Hague in 1852, is a painter of town-views, an illusive limner of bright sunlight on house-fronts, quite as topographical as Springer, but less colourful, less studied in his composition, painting the old buildings and squares and canals of our country cleverly and unemotionally, in a manner that is always reminiscent of his master, Christoffel Bisschop. Klinkenberg is a painter of whom one might have expected that he would have taken the excellent Jan Weissenbruch, with his fine, sound workmanship, for his guide in a style which, separately considered, has been produced by no later artist with the same amount of truth and value. However, he found himself and worked out his own ideas, which, if they do not fall within the domain of pure painting, are, in any case, popular.