"Flapdoodle" is a slang word used by Mark Twain in the 25th chapter of Huck Finn. The king and the duke are con men who are trying to bilk the Wilks' daughters out of their inheritance, $6000 in gold. They put on a great show of sorrow over Peter Wilks' death, claiming to be his long separated brothers from England. Huck sees the whole show put on by the king and duke as so much "flapdoodle," a word which could be replaced by baloney, balderdash, hogwash or similar slang words, meaning outrageous, obvious lies.
The word seems to have been common slang that was in use at the time of Twain's writing "The Adventures of Huckleberry Finn." Twain uses the word to great comic effect, because of the sound of the word itself, a nonsense word, like something a child might make up.