Following graduation from Oxford, Kearny joined a Royal Geographic Society expedition in the Peruvian Andes. He then worked as an exploration geologist for Standard Oil in the Orinoco jungles of Venezuela, where he became familiar with equipment and tools of the native inhabitants of the region. He later used the information gained from this experience to develop specialized jungle equipment for U.S. military forces.
In 1940, Kearny went on active duty as an infantry reserve lieutenant in the U.S. Army. Recognized for his knowledge of jungle travel and use of specialized tools and equipment, Kearny was soon assigned to Panama as the Jungle Experiments Officer of the Panama Mobile Force, and was promoted to captain. In that capacity he was able to invent, improve, and/or field test much of the specialized jungle equipment and rations used by U.S. infantrymen in World War II. Adoption of the jungle field ration and the jungle hammock as standard equipment by the US Army in World War II is credited to Kearny, along with improvements to many other items of tropical gear, such as the Panama-soled tropical boot and the machete. In recognition of his service, he was soon promoted to major and awarded the Legion of Merit.
In 1943, he married May Willacy Eskridge of San Antonio.
Kearny later volunteered for duty with the Office of Strategic Services (OSS), where he served as a demolition specialist in southern China in 1944. As Japanese forces threatened to overwhelm Chinese defenses in southeast China, he walked night and day to escape capture. After contracting a serious viral disease during that campaign, he was bedridden for many months and partially crippled for several years. After a long convalescence, he retired from active duty with the U.S. Army.
In 1961 he took a position doing civil defense research with the Hudson Institute. In 1964 he joined the Oak Ridge National Laboratory civil defense project. During the Vietnam War, Kearny served as a civilian advisor to the U.S. Army, making several trips to the theater of operations. He died in 2003.
In a New York Times obituary, his daughter Stephanie commented: "Throughout his life he believed in being prepared for trouble.
His other works include Jungle Snafus ... and Remedies, a book on the history of development of specialized equipment for use by military forces in jungle regions, and Will Civil Defense Work?