The story
* Most likely a pseudo-condensed pronunciation of kilometer, being a suitably short word emphasizing k+l instead of /keɪ/ alone (the same principle as with military spelling alphabets, but also clearly distinguished from kilo (/kiːloʊ/) for kilogram). * Possibly onomatopoeic of the sound of a military odometer. When a soldier would complete a mark, they would signal to their commander and denote movement of 1,000 meters by hoisting up their rifle and moving the gas regulator with their thumb, which made a "click" the commander could hear.
Etymology from Wiktionary, CC BY-SA 4.0.