After the outbreak of World War I, he was posted as a communications officer to the battlecruiser SMS Derfflinger, where he received promotion to Leutnant zur See in 1915.
From 28 September 1928 Kleikamp was the officer responsible for training and education on the cruiser Emden, before being appointed director of the Nachrichtenmittelversuchsanstalt on 11 February 1930.
He served in this position until October 1932, when he was appointed naval liaison officer to the Wehrkreiskommando I in Königsberg, having been promoted to Korvettenkapitän.
On 1 September 1939 at 04:45, Kleikamp gave the order for the attack on the Westerplatte and two minutes later the first shells left the barrels of Schleswig-Holstein's 28 cm guns.
After the invasion of Britain was cancelled, Kleikamp transferred to Naval High Command as Chef der Militärischen Amtsgruppe in Hauptamt Kriegsschiffbau, a position he held until 21 February 1943.
From March 1943 until the end of 1944, Kleikamp, having been promoted to Konteradmiral and ultimately Vizeadmiral, served as Kommandierender Admiral in den Niederlanden.