Here is part of the explanation for nekkid which I found on the site Word Detective.com. It is often paired with the term, as a jaybird.
The phrase “naked as a jay bird” means, of course, to be utterly without clothing. A “jay” is a species of songbird, probably most familiar to us as the blue jay, with its brilliant blue plumage and distinctively raucous call.
Just where the phrase “naked as a jaybird” came from is, however, a mystery. It has been in fairly common usage since the middle of the 20th century, and seems to be American in origin. Why blue jays, which are modestly covered with feathers, should have become symbols of stark nudity is anyone’s guess. The English have a similar phrase, “naked as a robin,” but that doesn’t seem to make any sense either.
I suppose it is possible that “naked as a jaybird” is related somehow to the use of “jay” in the 19th century for a hick or rube recently arrived in the city. This “jay” underlies our term “jaywalk,” meaning to cross the street in the middle of the block or in some other unorthodox fashion, supposedly as one unaccustomed to urban traffic rules might.
In any case, since we’re reduced to guessing, here’s mine. There are few birds more blatantly obvious than the male blue jay. Not only is Mr. Jay bright blue, not a common color for animals of any ilk, but he is also usually the loudest and most obnoxious bird in any given tree. As a symbol of that which is flamboyantly obvious, the blue jay takes the cake. “Naked as a jaybird,” therefore, might just be a colorful way of saying “blatantly and obviously completely naked.”
And in the Southern part of the U.S. sometimes the pronunciation of the work naked sounds like nekkid. The word nekkid (or that particular pronunciation of the word naked) is often attributed to hicks in the Southern U.S. And it just sounds so dadgummed funny.