The flatworms get their energy from algae that live inside their bodies, not from eating corals, coralline, or anything else desirable.
I wouldn't recommend a school of 6-lines for a few reasons. First is that they're hit or miss when it comes to eating them, usually more miss than hit. Second, they aren't likely to get along, especially as they get older.
Probably the safest way is to just siphon out all of them you find everyday for a week or so. I did a major WC two days in a row, siphoning out as many as I could as I went. That got the majority of them. Then everyday for the next week or two I just kept a turkey baster by the tank and every time I walked by I sucked out any I saw until they just stopped showing up.
Salifert also makes a product called Flatworm Exit. It works well and seems to be reef safe, but when the flatworms die they release a toxin, so you have to do some work with that method too. Beforehand you should siphon out as many as you can see, then mix up water and be ready to do a large WC after the treatment. You also need some fresh carbon. Usually it's recommended to do two treatments about a week apart.
Generally, biological controls don't work. Six-lines probably have the best record of the predators, but they probably don't solve the problem in even 50% of the cases. Mandarins are significantly worse, and the flatworm eating slug Chelidonura never works.