The problem with Mandarins is that they mainly eat pods
. Some will eat prepped food like frozen brine shrimp, but it's rare. They also eat a lot. A LOT. From what I've been told by people much more knowledgable than me, and from my own observation, if the Mandarin eats flatworms... it's more on accident than intentional. Chances are, a Mandarin would just starve to death in your tank without making any real impact on your flatworm population.
Wrasse would be a better bet, because they aren't as choosey about their food. Meaning, it wont starve to death. But still, there's no guarantee that it will eat your flatworms.
These guys are supposedly great for eating flatworms.
They'll eat them until they can no longer find them, at which point they starve and die. Problem is, there's usually one or two flatworms hiding out in your live rock that it couldn't find. They'll just reproduce and your back to where you were.
Personally, what I would do is this...
Get some airline tubing, put a filter sock on one end, and us the other to syphon out as many flatworms as you can. This way they get caught in the filter sock and you don't lose any water. After you've got as many as you can, treat the tank with flatworm exit. Doing that before treating with FWE, benefits you in two ways.
1) You reduce the amount of toxins released by dead flatworms by a huge amount.
2) It's much easier to kill 20 flatworms than it is to kill 1000. (obviously guessing on numbers)