It now appears that the situation is more convoluted, and that I'm redoing the work of someone who also stumbled upon the quote -- 108 years ago!
In a letter published in Nature (July 3, 1902), Hiram Stevens Maxim -- the inventor of the automatic machine gun, the mousetrap, amusement-park airplane rides, and possibly the lightbulb -- asked the editors about the source of Kelvin's wing-beat-changes-the-Universe quote -- only in the version Maxim read (from William Stanley) it was a mosquito wing doing the Universe-beating:
Mr. William Stanley, an American philosopher and engineer, said a few days ago that the grandest words ever uttered by any man on this planet were spoken by Lord Kelvin when he said that if all the matter in the Universe were reduced to its ultimate atoms and equally divided through all space, the disturbance caused by the beating of the wing of one mosquito would bring about everything that we find in the material Universe to-day. I have written to Lord Kelvin asking him where I can find some account of this, but he denies that he ever said anything of the kind. However, as Mr. Stanley declares that it appeared in Nature, perhaps you can put me in the way of getting a copy of the paper which contains this remarkable utterance, which, by the way, is quite true, and if Lord Kelvin did not say it, I only have to say that he might well have been the author.
Hiram S. Maxim,
18 Queen's Gate Place, London, S.W., June 25.
A Google book search turned up nothing in Nature from Kelvin on this subject, but searching for a quote based on a paraphrase that may include the wrong order of insect isn't exactly a science, so I could be missing it. (Also, if I may gripe, Google treats issues of many older periodicals as if they are different editions of the same book, showing only the newest issue that matches the query, making searches aggravating.)
While this almost certainly excludes Kelvin from being the source of the Butterfly Effect's specific protagonist, and possibly his general insectile contributions to the field of chaos theory if his memory was correct, it still calls into question Ray Bradbury as the ultimate source of the lepidopteran imagery.
But more interestingly, the butterfly seems to have originated out of a paraphrased-quote-based game of telephone -- where the flap of a tongue can turn "tornado" into "Texas" -- making it an example of its own effect.
P.S. If you came here looking for the band called the Mosquito Effect, you are in the wrong place.