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Jehochanan (Hebrew)
--> Johannes (Greek)
--> Johann/Johan (German / Low German)
--> Jan (Flemish / Frisian / Low German)
--> Janken/Jankin ("little Jan", Flemish / Low German)
--> Jackin (Flemish)
--> Jack (Flemish / English)

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Another short form of Johann is Jon/John - so there you've got the connection.
By the way - all the J's are pronounced like Y, even Jack and John, except in English.

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Jan and John can be short for Jonathan as well.

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Another way "Jack" came to the English language was via French "Jacques" (French form of Jakob).

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Regards, Satu