He studied under Peter Janssen, among others, at the Kunstakademie Düsseldorf from 1879 to 1881. After completing his education he became a professor at the Kunstakademie and taught there until 1889, when he moved to Berlin. There he continued to teach at the local Kunstakademie.
From 1915 to 1924 he was president of the Hochschule für Bildende Künste in Berlin. He also became a member of the Prussian Academy of Arts, and gave drawing lessons, notably to Prince August Wilhelm, son of Wilhelm II.
Kampf joined the Nazi Party soon after the Nazis seized power. In 1939's "Great German Art Exhibition" (Große Deutsche Kunstausstellung) at the Haus der Kunst in Munich, he was represented by numerous works. In 1939 he received the Adlerschild des Deutschen Reiches with the inscription "To the German painter" (Dem deutschen Maler).
In 1944, Kampf was one of 24 artists, architects, authors, composers, actors, and singers added to the "Special list" of the Gottbegnadeten list, meaning he was considered absolutely indispensable.
- Ernst Klee: Das Kulturlexikon zum Dritten Reich. Wer war was vor und nach 1945, S. Fischer, Frankfurt am Main 2007, p. 294.
- Kunst im 3. Reich. Dokumente der Unterwerfung. Catalog of the Frankfurter Kunstvereins, 1974.
- Berthold Hinz: Die Malerei im deutschen Faschismus. Kunst und Konterrevolution. Hanser, Munich 1974, ISBN 3-446-11938-8.
- Hermann Hinkel: Zur Funktion des Bildes im deutschen Faschismus. Anabas, Steinbach 1975, ISBN 3-87038-033-0.
- Reinhard Müller-Mehlis: Die Kunst im Dritten Reich. Heyne, Munich 1976, ISBN 3-453-41173-0.
- Otto Zirk (1977), "Kampf, Arthur von", Neue Deutsche Biographie (NDB) (in German), 11, Berlin: Duncker & Humblot, pp. 90–91