You can find some information on this matter by checking the website for earliest known uses for some of the words of mathematics maintained by mathematician Jeff Miller. You can also find information on the etymology of the word "kernel" in standard dictionary sources.
Writing in French, Fredholm (1903) used the word "noyau" (core) and Hilbert (1904) adopted this term but wrote in German, yielding the German word "kern" (core). These terms were used in the context of writing about integral equations in functional analysis. Shortly after this, Bôcher (1909), writing in English, uses the term "kernel" to refer to the same objects. The term then spreads through the English-language literature on functional analysis, Fourier analysis, and later, probability and statistics.
According to the above-linked dictionary, this word derives from Old-English and Proto-Germanic. It can refer either to a seed, or to the core, center or essence of an object. The linguistic similarity between the German "kern" and "kernel" appears to be due to similar historical derivations. The word "kernel" is alleged to have derived from a hypothesised (reconstructed) Proto-Germanic word "kurną" (corn). So, based on this history, it seems that etymologically, the word "kernel" refers to a seed, core or essence, and is based on the Anglicisation of an old German word for corn.
UPDATE: This answer has been edited heavily to reflect new information that was brought to my attention by users cbeleites and R.M. I initially thought this may have been a recent Anglicisation of the word "kern", but the dictionary sources suggest that the word "kernel" in English is very old. I am not a linguist, so I am merely setting out information from the above sources.