Wiktionary says it is either likely a pseudo-condensed pronunciation of kilometer or onomatopoeic of the sound of a military odometer.
Though kilometers are not commonly used to measure distance in the USA, “klick” is commonly used by the US military, which uses the metric system almost exclusively in order to facilitate communication with allied forces.
Here’s an example of the word being used in the film Apocalypse Now:
We’re going up river about 75 klicks above the Do Lung bridge.