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The correct abbreviation in the SI system is kJ, that is small k, large J. It is the convention to use capital letters for units named after real people. This includes A for Ampere, K for Kelvin (degrees absolute), N for Newton, J for Joule, W for Watt, Pa for Pascal, Hz for Hertz, V for Volt, F for Farad, H for Henry.
Prefixes seem not so logical. Thus we use small k for thousand times, but large M for million times, small m for one thousandth, and greek mu for one millionth!
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