Flannuss Broadwing tends to circle the island seen on the map. If you can't see him when you arrive there wait and he will eventually patrol.
Without anti-caster skills like Backfire he can be very hard to kill and thus it is recommended to take him down as soon as possible. If you see him approaching when you are fighting another group, retreat right away since he is surrounded by 4-5 high damage elementalists and they won't go down easily with him around. When fighting him, try to spread his forces out, so his Karei's Healing Circle won't be as effective.