No it will not. Phoebe reads "During this turn, damage from your Pokémon VMAX's attacks isn't affected by any effects on your opponent's Active Pokémon." Specifying Active Pokemon means Phoebe will never interact with targets on your opponent's bench. Even if Mew is active, Bench Barrier is not an effect on Mew, it's an effect on your opponent's benched Pokemon, meaning that while Mew is active, Phoebe still should not change any interaction between Rapid Flow and Bench Barrier.