Richard Kulka, son of the cloth mill owner Leopold Kulka and Charlotte, née Scheuer, spent his youth in the Austrian-Silesian town of Jägerndorf (now Krnov, Czech Republic), before leaving in 1881 to study in Vienna. After becoming a doctor of law in 1890, he opened a law office in Vienna's 6th district. He had many interests and was a member of the Anthropologische Gesellschaft (Anthropology Society), the Verein für Volkskunde (Folklife Association) and the Gesellschaft von Amateur-Photographen im Österreichischen Touristen-Klub (Amateur Photography Society in the Austrian Tourist Club). He also collected nineteenth- and early twentieth-century Austrian art. He was particularly interested in landscape painting, and his collection contained mostly landscapes by plein-air painters such as August von Pettenkofen, Jakob Emil Schindler and Tina Blau, and the "Stimmungsimpressionisten" (mood impressionists) Theodor von Hörmann, Eugen Jettel and Richard Russ. He also owned several works by Rudolf von Alt and one by Friedrich von Amerling. One of the main works in his collection was Wilhelm Richter's 1849 Portrait of August von Pettenkofen.
In 1921 was admitted to the Wiener Künstlerhaus, where he bought and sold works. He had left the Jewish religion in 1902 and died in 1931, unmarried and childless, in Vienna. He bequeathed his assets, including the collection of around 150 paintings, to his sisters Adele Kulka and Valerie Heissfeld. He also bequeathed items to the Historisches Museum der Stadt Wien and the Paintings Gallery of the Akademie der bildenden Künste in Wien (Academy of Fine Arts in Vienna).