I've heard rumors of a target mandarin and a sixline wrasse eating them. If you want something that will hands down eat them you could get a blue velvet nudibranch, but you will need to find it a new home when your flatworms are gone.
Its been hit or miss with me in the past... I have had 6 line wrasse eat them and then others would starve before eatting a flat worm. Also, to my knowledge if a 6 line eats a bunch of them in a short time then the fish will die from there toxins. I do believe this because when I had flat worms in a tank a while back the three 6 lines that I went through that would eat them all died within a couple days of eatting a bunch of flat worms.
I have a sixline and I don't see any flatworms. I now dip every coral so they shouldn't end up in the tank but when I first started getting corals I didn't dip but I give all the credit to the sixline
Some wrasses like a 6 line, yellow coris, etc. Dragonettes (Mandarin, scooter blenny) and Lemon Damsels will all eat flatworms. Some are better than others and it depends on the individual. I have had good luck with my xxl scooter blenny.
yellow coris is hit and miss
i had one that did very well in my frag tank but when i set up a display and got them i got another yellow coris because of my previous experience and he did nothing