Green’s Dictionary of Slang

flush adj.

drunk.

1737		B. Franklin ‘Drinkers Dict.’ in Pennsylvania Gazette 6 Jan. in AS XII:2 91: They come to be well understood to signify plainly that A MAN IS DRUNK. [...] Flushed.
1848		‘Ned Buntline’ Mysteries and Miseries of N.Y. V 82: I saw him, but he was very much flushed with liquor!
1914		Joyce ‘A Little Cloud’ Dubliners (1956) 73: I met him one night in London and he seemed to be very flush.
1933		‘William Juniper’ True Drunkard’s Delight 225: Our tippler may further be [...] flushed.
1956		‘James Updyke’ [W.R. Burnett] It’s Always Four O’Clock 82: The guy and one chick were really boiled, staggering and holding onto each other. The second chick was just a little flushed up.