Hey Guys IMO/IME there is no real issues in having Dragonets with either Flasher or Fairy Wrasses since they're open water plankton feeders,its the smaller Halichoeres species like 4 & 6-Line, Yellow Coris, Radiant etc... that actively hunt the same substrate. My Radiant will occasionally pick on my Target Mandarin but usually gives up after a few failed attemps to provoke a flight response. Food-wise he prefers a little larger items and basically ignores the tiny pods the Mandarin actively hunts. The larger of the Halichoeres species are definitely to aggressive to mix with Dragonets or Flasher/Fairy Wrasses.
Cheers, Todd