This has to be American and probably cowboy in origin eg Billy the Kid, the Sundance Kid, Kid Curry (who rode with Sundance) etc and I would guess it is from age or youthful appearance though I cannot find this attested to online in a cursory search. (The poetic name Sundance turns out to be from his spending 18 months in Sundance Jail in Wyoming says wikipedia.) Could anyone have gotten such a nickname at this time or just felons?

David Maurer in The Big Con lists early 20th century American conmen such as the High Ass Kid, Yellow Kid Weil, the Sanctimonious Kid, the Hashhouse Kid, the Christ Kid, and the Honey Grove Kid. These people are probably not all youngsters so the appellation may have acquired ‘outlaw chic’ by this stage. Various rappers call themselves Kid something too in a similar romanticising process I’m guessing.

White music has the ageing Kid Rock and there was a Canadian radio DJ in the UK in the ‘70s called Kid Jensen from his youthful looks and coolness though he dropped this later, hopefully out of embarrassment. Steely Dan has a song Kid Charlemagne from the ‘70s.

Your thoughts, if any?

The entry in OED for kid, n.1, 5b is interesting in this regard.

b. In low sporting or criminal circles: A term of admiration for an expert young thief, pugilist, etc
.
1812 J. H. VAUX Flash Dict., Kid,..particularly applied to a boy who commences thief at an early age; and when by his dexterity he has become famous, he is called by his acquaintances the kid so and so.

Thanks, aldi, that seems to explain it. It is interesting no Kids have entered British folklore.

Captain Kidd? ;-)

The tradition is still very much alive. “Kid Delicious” is the monicker of Danny Basavich a pool player from New Jersey. According to Basavich in a radio interview, the moment he beat Kid Vicious after an extremely long match (I think he said his longest match ever was 60 hours), an onlooker quipped, “Kid Delicious just beat Kid Vicious.” Basavich is more than a little portly.

At least in Northern England in the sixties, “kid” was regularly used for younger siblings. “Our kid” was more or less standard when/where I grew up for a younger brother. I have always thought that it is simply an extended use of the term for the young of certain animal species (deer, goat...)

It’s still used in northern England.

I found this comment on Much Ado About Nothing from Shakespeare’s Himself Again, or The Language of the Poet Asserted by Andrew Becket, published 1815.

Claud. “We’ll fit the kid-fox with a pennyworth ...”

“We’ll fit the kid-fox & c.” The sense of kid-fox here is mistaken by the commentators.  A kid-fox is a cunning, artful, knowing fox.  See Spenser. 
The lines from Chaucer show that it has with him the same meaning.  Thus a kid-napper, or as it should be written, a kid-nabber, is not a catcher of kids or children, as is usually imagined, but a cunning, artful, catcher.

It seems as if this sense of cunning was eventually applied to artful children.  The obsolete adjective kid, which has the sense of notorious, is related to the verb kythe/kithe, according to OED.  Kythe means made known.