Flamingo Tongues are ovulids, not cowries, and they feed on gorgonians. Real cowries, like the ones in the photo at the top of this page (and in my avatar) are pretty much reef safe, none of them intentionally feed on either soft or hard corals. Neither cowries nor ovulids are filter feeders.
If the cowry FREAK* has is only an inch long, it's neither Cypraea zebra nor C. cervus, as these cowries average about 3 and 4 inches respectively. If it's brown with white spots, but more rounded instead of elongate and cylindrical, it's probably Cypraea (Lyncina) vitellus, the Pacific Deer Cowry. It should be reef safe, but as for sliming the tank, the same applies to this species as to all the others: if you see a lot of strings of slime floating in the tank after you introduce it, you should probably try to get them out of the tank, as best you can. The slime isn't toxic, but may coat the gills of the fish if there is enough of it.
The cowry in your photo at the top of this thread is Cypraea cervinetta, the Panamic branch of the C. cervus/C. zebra complex, which are Caribbean/Atlantic species. A tiny dwarf of this species is about 1.5 to 2 inches long, and they grow over 4 inches in length. If your cowry has teeth on the bottom and spots on the dorsum, it is an adult, and won't grow any larger than it's present size.
Cheers,
Don