Upon commissioning, Kıvrıkoğlu underwent his officer's basic training at the Artillery Branch School in 1957.

He spent the next eight years in a variety of artillery units as platoon and battery commander positions.

After graduating from the NATO Defence College in Rome, Italy, he was promoted to brigadier general in 1980 and assigned to Supreme Headquarters Allied Powers Europe (SHAPE) in Mons, Belgium, where he served as the chief of operations center from 1980 to 1983.

In 1984, Kıvrıkoğlu was promoted to major general and assigned to NATO Allied Land Forces South-Eastern Europe (LANDSOUTHEAST) in İzmir, where he served as chief of staff.

There are rumours that Kıvrıkoğlu survived an assassination attempt in 1997's "Toros-2/97" exercise in Northern Cyprus.