I think what most people refer to as a flower anenome is an Actinia species (possibly equina??) I don't have any experience with them in reef tanks but I have kept beadlet anenomes from the same genus in coldwater tanks and had them successfully reproduce quite a lot. However I wouldn't say this...
If it makes you feel any better I was at a public aquarium a few months ago, one of the tanks was completely infested with aiptasia so I thought to myself wow they're really plagued by the things I wonder whats actually meant to be in here since nothing moving was evident. I looked at the tank...
Any chance its a basket star or crinoid type thing or any kind of brittle starry thing? or perhaps one of those upside jelly fish (casseopia I think they're called). Probably wrong but thought it might be worth throwing in some possibilities.
Wayne