In a manner characterized by flinching; showing hesitation, fear, or reluctance.
From 'flinching' (present participle of 'flinch') plus the adverbial suffix '-ly.' This creates an adverb describing the manner or way of performing an action.
You almost never see 'flinchingly' used outside of literature because we usually describe flinching behavior through actions rather than adverbs—but novelists love it for showing internal conflict through physical reaction.
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