“An arbitrary formation”, solemnly state those dictionaries that are not content with the bland and unhelpful “origin unknown”, though they all do give its meaning of nonsense or twaddle. That’s not quite the whole story: the older and rarer fadoodle had much the same sense. And flapdoodle, though perhaps with a different origin, is recorded as current in the eighteenth century for the male and female naughty bits.
Whatever its source, it’s usually and reasonably taken to be an American word. Which makes it slightly odd that the first known example is from a book by the English writer Captain Frederick Marryat, best known for Mr Midshipman Easy and The Children of the New Forest. His Peter Simple was serialised in the Metropolitan Magazine in 1832–33: “‘The gentleman has eaten no small quantity of flapdoodle in his lifetime.’ ‘What’s that, O’Brien?’ replied I. ‘Why, Peter,’ rejoined he, ‘it’s the stuff they feed fools on.’ It may be relevant that Captain Marryat’s mother was American, from Boston, and that this sense of the word is rare.
Nearly all its appearances in the next few decades are certainly from US sources, as in this Wisconsin newspaper piece dated 1859, “They say that no such flapdoodle can be forced down the throats of the intelligent people of Wisconsin.” By the 1880s, it was widely known, the verb to flapdoodle had appeared, and an editor of a newspaper in Kansas objected to the flapdoodlish editorials of a rival journal.
Variations abounded, such as doodleflap and flamdoodle. The Fort Wayne Sentinel printed a story in 1900 about an old man who could not be persuaded of the value of these newfangled banks. “The building looks all right from the outside, but when a critter gits inside it’s flipdoodle checks and flamdoodle receipts and writin’ names, and no hollerin’n or drinkin’n or shootin’. I’m too old fur flipdoodle and flamdoodle, and I’ll bury my money in a hole in the ground and keep on in the ole way!”