It seems that Jack comes from adding a french diminutive (-kin), to Jean (John).
http://en.wikipedia.org/wiki/Jack_%28name%29
Rather, it is believed that "Jack" is the result of adding the French diminutive suffix "-kin" (much like the German "-chen") to the name "Jean," which is the French form of the English "John", or "Jan," which is a shortening of the German "Johann." The result would have pronounced as "ZHANG-kin," with the "n" being nasalized, and thus later omitted by Anglophones without much difficulty.
In the case of Dick, it's a rhyming nickname for Rick, which is a shortening of Richard
http://www.thinkbabynames.com/meaning/1/Dick
A rhyming nickname from medieval times. Richard (Old German) "dominant ruler", was shortened to Rick, then rhymed to Dick, and variants like Dickson and Dix (which is also the French word meaning "ten") followed.
