If your Mienshao already has this move, the other Pokemon would do better with a different move. Also, the point of Fake Out is to be used in double/triple battles, so you can interrupt a Pokemon, while another Pokemon of yours does something that's really gonna have an impact, something like a status or high damaging move, so if one of yours already has Fake Out, it is already enough.
The point of using it is to intercept and interrupt an enemy that you think that will use a very powerful or important move on the first turn so it can't use it, while the rest of your team can actually use their moves on the first turn.
If both you and your enemy's other Pokemon can't use another move on the first turn, then you and your foe are in the same boat, because they will just use the move they would have used on the first turn on the second turn, and you have wasted your opportunity to do something while he was interrupted.
If there are double battles, one Pokemon with Fake Out is enough, if it is in triple battles, depending on your strategy, maybe two could have that move to stall the enemy, while the third Pokemon does something that is going to be very powerful or important.