Green’s Dictionary of Slang

foolish, stupid.

1849		Sam Sly 3 Feb. supp. 5/3: He advises the flat-headed cooper, of Hoare’s brewery, not to fancy he can sing.
1889		Music Hall & Theatre Rev. 23 Mar. 86/2: [A]ll the passion such a flabby, flat headed, tailor-built personage was capable of.
1890		Aberdeen Jrnl 29 Jan. n.p.: The man who would feel flattered to be called level-headed would object strongly to being called flat-headed.
1903		‘Hugh McHugh’ I Need The Money 76: Didn’t I land your flat-headed old uncle for a shoe shine five minutes after I struck the grounds!
1947		S. Lewis Kingsblood Royal (2001) 318: The flat-headed but sturdy W.S. Vander as war-chief.