The name Jack came from a Middle English word, “jakke,”
used to refer to any male, particularly those of the lower classes.
Because Jack was so often used to refer to social underlings, it was eventually used to refer to useless objects.
Eventually, it began being used as a term for very little. The phrase “you don’t know jack” (with or without the expletive) has been used for decades to say someone knows very little. Yes, it seems to be a bit of a double negative, but expressions are commonly created and spread without any consideration for proper grammar.