Flinching rhymes with:
unflinching, clinching, lynching, unflinching, clinching, inching, lynching, pinching, unflinching, branching, bunching, clinching, crunching, drenching, entrenching, inching, launching, lunching, lynching, munching, pinching, punching, quenching, ranching, retrenching, stanching, unflinching, wrenching
Flinching sounds like:
filmmaking, flanigan's, flanking, flinging, flunking