He was likley born around 1890 in what is today Czechia, but later lived and worked in Paris. Kromka moved among the bohemians of the time, and belonged to the group of Czech artists centred around František Kupka in Montparnasse. Kromka was primarily a musician, and only began making abstract paintings around 1925. In the 1920s, he took part in an exhibition at the Galerie Matignon in New York. After France was occupied, Kromka was arrested by the Nazis in 1942 and deported to Auschwitz, where he was killed.