Unflinching rhymes with:
flinching, clinching, flinching, lynching, clinching, flinching, inching, lynching, pinching, branching, bunching, clinching, crunching, drenching, entrenching, flinching, inching, launching, lunching, lynching, munching, pinching, punching, quenching, ranching, retrenching, stanching, wrenching