Some Tea Party spam recently came my way, bringing with it a curious neologism. "You really believe that?" scoffed the author. "Oh Ya, and Obama is a conservative! Hahahaha! What flat-trap nonsense!"
I guessed that flat-trap might be an eggcorn for claptrap,though I couldn't immediately come up with another relevant citation for flat-trap. (Google offered up a Melbourne band, some glue traps for mice, and several physics papers with titles like "Superfluidity of two-dimensional excitons in flat and harmonic traps.") But you could get from claptrap to flap-trap quite easily, I thought, if you took "clap one's trap" to be a variant of "flap one's trap (or one's gums)," meaning "talk nonsense."
But was that in fact the root sense of claptrap? Not even close. Claptrap, says the OED, is a theater term from the early 1700s, meaning "a trick or device to catch applause; an expression designed to elicit applause." The first citation is a dictionary definition dated 1727-31: "A Clap Trap … a trap to catch a clap by way of applause from the spectators at a play."
That rather literal meaning fits nicely into the latter part of the English theatrical era that gave us characters named Marplot, Aimwell, and Lady Wishfort. But the evolution of claptrap into its modern meaning is also pretty seamless: by the early 19th century it means "language designed to catch applause; cheap showy sentiment" (OED), and that sense generalizes easily over time to "nonsense, rubbish."
Meanwhile, shut one's trap had been used since the 1770s; flapping one's mouth came along in the early 20th century, giving rise to flapping one's trap or gums. So flap-trap, though coined by a different method from claptrap, is just as plausible. But flat-trap? I still can't figure out a way to make that "flat" fit the idiom.