AFAIK Flash does support colour management since Flash 10, but it defaults to being turned off, and many sites don't use it. I don't know if adoramapix uses colour management in Flash, but might be worth checking their forum or help. If there's no mention of Flash colour management then presumably they don't do it!
I regard Flash as a pile of poo (that's a technical term) and don't use it unless my life depends on it.