Where does “unflappable” come from?

I need to work through this chain carefully, as it appears problematic. The chain provided seems malformed—it lists "Latin unus" and "Proto-Indo-European óynos" early, then later includes "Latin -abilis" and various PIE elements, with some repetition ("Proto-Indo-European ano-" appears twice). The chain doesn't clearly show how these elements combine to form "unflappable." A reliable etymology for "unflappable" would trace: English unflappable ← un- + flappable ← flap + -able. The "-able" suffix comes from Old French and Latin "-abilis," but the chain as given doesn't support a coherent path from the listed elements to this word. Given the instructions to "state only what the chain supports" and "do not invent," I cannot responsibly construct a sentence that would misrepresent the etymology by forcing these

unflappable (English): Remaining composed and level-headed at all times;...