He fought with the "Iron Division," but left the army in April 1920 and settled in Danzig where he worked as a mechanic and ran a car dealership.

On its formation on 6 September 1939, Kaul was named the first Higher SS and Police Leader "Südwest", based in Stuttgart, while retaining his Oberabschnitt command there.

In the spring of 1943, Kaul had a falling out with SS-Obergruppenführer Gottlob Berger, the head of the SS Main Office, and was relieved of his posts on 21 April 1943.

For a time, he ran two horse breeding farms and then, in September 1944, he trained at the SS artillery school as a Waffen-SS Sturmbannführer.

He took command of an artillery regiment in the 22nd SS Volunteer Cavalry Division Maria Theresia in November 1944, and died on 25 December 1944 during the siege of Budapest.