He graduated from the Norwegian Military Academy in the same class as Vidkun Quisling. He had a military and civil career, and was an assistant secretary in the Ministry of Defence (headed by Quisling from 1931 to 1933) in 1940. He was also a member of Quisling's Fascist party Nasjonal Samling.
On 25 September 1940, Kjelstrup was hired in the Ministry of the Interior as head of the civil administration of the Norwegian Army and Navy. In 1941 he agitated for the formation of the Norwegian Legion (German: Freiwilligen Legion Norwegen), a Foreign Legion under Waffen-SS. He served as its chief of staff in Norway, from 29 June to 1 December 1941 with the rank of Colonel. The staff was soon dissolved because Germany wanted less Norwegian control. The Norwegian Legion existed until 20 May 1943.
The German occupation ended on 8 May 1945, and as a part of the legal purge in Norway after World War II Kjelstrup was sentenced to eighteen years of forced labour. He served some of the sentence before being released. He was afterwards active in the organization Forbundet for sosial oppreisning and wrote in the newspaper Folk og Land. He died in 1961.
- Ringdal, Nils Johan (1995). "Kjelstrup, Finn". In Dahl, Hans Fredrik. Norsk krigsleksikon 1940-45 (in Norwegian). Oslo: Cappelen. Archived from the original on 15 March 2012. Retrieved 5 April 2010.
- "A relatively peaceful life in the tropics". Museum of History and Culture, University of Oslo. Retrieved 19 May 2012.
- no:Knut Flovik Thoresen, Retrieved[better source needed]
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