I've found these ( and all Flan that I have fought and killed ) to be water-based. They drop water crystals, and show a definite weakness to thunder-type spells.
For example, during Besieged, my typical spells ( Blizzard IV, Fire IV and the like ) will do anywhere from 100-200 damage, which is far less than they would against your typical exp mob. However, when fighting these, Thunder IV hits for 1300, and Burst II for 1500+. Needless to say, when everyone else is hitting it for 20-30 and it's hitting them back for 200, I pulled a substantial amount of hate and ended up inspecting the tile in Al Zahbi.
For maximum damage and effectiveness, go for Thunder-type spells while fighting these during Besieged. Just <Take care.> when you do so, and remember that Reraise is your friend.