Flunking rhymes with:
plunking, spelunking, debunking, junking, plunking, spelunking, banking, blanking, blinking, clanking, cranking, debunking, drinking, flanking, franking, honking, junking, linking, nanking, nonbanking, outflanking, planking, plinking, plunking, ranking, reinking, rethinking, shrinking, sinking, spanking, spelunking, stinking, tanking, thanking, thinking, unthinking, winking, yanking
Flunking sounds like:
filmmaking, flanigan's, flanking, flinching, flinging