Green’s Dictionary of Slang

flat v.

[SE turn down flat / a flat refusal]

(US) to reject a suitor.

Show quotations
[US] in N.E. Eliason Tarheel Talk (1956) 271: Widow Yarborough has flatted the little Captain.
[US]Schele De Vere Americanisms 602: To flat, in the West, means to jilt, and is probably derived from another slang phrase, to feel flat, denoting the depression which is apt to follow such a disappointment.