As Opus said, treating it with Flatworm Exit *outside* of the tank will be the best way to be sure. If they all fall off when you swish the frag in the bucket at the end of the treatment it is flatworms.
Sure looks like the ones I have killed in the past.
They are called red planaria but the ones I have seen have always been that pretty purple color.
Google cures for a while. Read up, there is plenty of info out there.
Have a lot of water premixed before treatment of the tank because the dead flatworms release a very strong toxin that can kill your fish and other corals.
Our favorite LFS and several others locally have a problem with them. It is a very common issue.
They are easy to surpress but difficult to eradicate completely. Then it's easy to get out of hand again.
Another good reason to dip all corals before adding to your tank. Even from good sources.
A little late, but it is the reason I dip corals now.
[emoji53]
Springeri damsels, blue velvet slug (very poor shipper), yellow damsels *should* eat them and have been effective in suppressing them in our tank.
The velvet slug is cool and a pretty addition to your tank. But it dies from starvation when it can't find any more nearby.
Springeri damsel stays small and calmer than the yellow damsel was.
Springeri is still in our tank.
Second pic is from the web. google red flatworms.