https://www.youtube.com/watch?v=AjTt2UxKvCM

This is the rotation I use as OT for 3x FC, but it requires a pre-Vengeance and an RI. Dunno how good it would be as a MT rotation (I don't run with a NIN).

Without using Vengeance you would do something like:

HS -> Maim -> Eye -> [Brutal] -> HS -> Maim -> [Pot] -> Eye -> IR -> Fracture -> HS -> Berserk -> FC -> Infuriate -> FC -> [RI] -> SS -> BB -> HS -> Maim -> SE -> Fracture -> FC -> Pacified

Use Brutal Swing whenever it comes back up, which should be somewhere in the Berserk window. The only problem with this is I have no idea how powerful NIN's aggro generation tool is, and this is starting in Deliverance and doing 2x SE before 1 BB (if you don't, Eye will fall off, but I guess if you coordinate with your NIN you could fix that). If you manage to not lose aggro, this will give you 2 fully buffed FCs and 1 Berserk buffed FC. If nothing else, that should explain the basic principle behind getting 3x FC without using Veng + RI.