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English is originally a Germanic language, with lots of influence from French after 1066, OK? In German, one way of forming a diminutive is to add -chen to the noun or name, like Grete becoming Gretchen. And the English version of -chen used to be -kin or -kins. You get it in surnames like Perkins (= Belonging to/Descended from Little Peter).

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I would be amazed if it still existed as a diminutive among English-speakers who just used it spontaneously; people who know about the history might use it as a joke: Go and do your homework, Tracykins.