Flatworms are a confusing group to research, mainly because there is not much information on the types and taxonomy and we have a habit of referring to the same worm with fifty different names. There are probably a few mistakes in this article, but I tried my best!

Removal should be looked at individually, as I have just given a brief idea of what I have seen to be recommended. Important to note: Many flatworms release toxins when they die, which can be a problem, for obvious reasons.
For most flatworms I would recommend starving them out first, to reduce the population, then manual removal.
If that isn't possible, there are chemical methods for removal such as flatworm exit, flatworm stop etc, though this usually requires a large water change after.
If the flatworms are ones that cover corals, dipping the coral, every 2-3 days for as long as you deem necessary/stop seeing flatworms (and a bit after that) Usually for around two weeks.
There are five major ways to remove/reduce flatworms, in no particular order: dipping, manual, chemicall, biological(fish/inverts that eat flatworms) and starvation.

Photos are not mine.

  1. Acropora Eating Flatworm
Classification: Platyhelminthes: Polycladida: Prosthiostomidae:prosthiostomum acroporae
Harm: Eating the coral's tissue and laying their eggs around the base of their skeleton.
Size: Up to 6mm
Colour: Brown/orange
Removal methods: Dipping, Manual(eggs) and Biological(Wrasses).
https://reefstable.com/solutions/pests/acro-eating-flatworms
Other:
Photo: First two photos show AFEW, the last
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  1. Euphillia eating flatworms
Classification: Platyhelminthes: Polycladida: Prosthiostomidae: Amakusaplana acroporae (Maybe, we don't know exact specie)
Harm: Consume the coral’s tissues and introduce harmful pathogens.
Size: 15mm
Colour: Transparent/Brown tinge
Removal methods: Dipping and Manual(eggs).
Other:
Photo:
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  1. Ghost Flatworm
Classification: Maricola Planarian triclad
Harm: Neutral but eat copepods
Size: 13mm
Colour: White/clear
Removal methods: Manual removal, chemical removal
Other:
Photo:
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  1. Convolutriloba sp. (Info from retrogemma)
Classification:Xenacoelomorpha: Acoela: Convolutidae: Convolutriloba: Amakusaplana acroporae
Harm: Consumes pods and can starve corals of sunlight
Size: 10mm
Colour: Reddish-brown
Removal methods: Dipping, chemical, manual.
Other: Redbug, red planaria, rust flatworm, or simply red flatworm
Photo:
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  1. Waminoa sp
Classification: Xenacoelomorpha: Convolutidae: Waminoa
Harm: Eats coral mucus
Size: 3-4mm
Colour: Orange-brown, often with white ring.
Removal methods: Chemical removal,
Other: Hosts one of two types of dinoflagellate.
Photo:
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  1. Leopard flatworm
Classification: Pseudocerotidae: Polycladida: Pseudobiceros pardalis.
Harm: feeds off of injured animals, bryozoans and soft corals.
Size: 20-50mm
Colour: Reddish-brown with large orange and small yellow spots. Small white spots
Removal methods: Manual removal.
Other: Can swim.
Photo: The photo of the white is this flatworms underside.
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