She turned it down flat.

Literal

She [topic-は] firmly refused.

きっぱり is a 擬態語 (state mimetic) for doing something cleanly, decisively, and with no room for negotiation — a clean break, no hedging, no leaving the door open. Pairing it with 断る ('refuse, decline') gives 'refuse flatly, refuse outright.' The mimetic doesn't describe the sound of the refusal but the manner — sharp, unambiguous, no follow-up. Useful contrast with the softer はっきり (clearly stated) or やんわり (gently softened); きっぱり is for refusals you don't want misread as wishy-washy.