Demolishing Strike if available
It's very simple, but I could add more to the rotation. But this would not increase FFXIV Gil DPS because the damage each ability that occupies a certain stage in the class mechanic system does roughly the same DPS.
Some abilities distinctly require a shield equipped or a great-weapons, both exclusive to each other, so different Black Orcs have a tendency to have different rotations.
I've been playing as a tanking Black Orc trying to keep others f Aion harm. But a DPS Orc with the same equipment (except for the weapon) and of the same rank who hasn't used any specialization points could use a rotation like:
Demolishing Strike if available
Follow Me Lead (Leads to Da Gud Plan, Path of Da Boss)
Trip 'Em Up (Leads to Da Best Plan, Path of Da Brawler) or Right in Da Jibblies if available
Taunt
Da Big 'Un (No Plan After Dis, Path of Da Boss)
Some of these abilities have buffs which apply to you and your allies. Both these rotations are the fastest way of cycling through the Black Orc Builder stages whilst making use of other useful abilities that have no effect on the Build stage.
As a tank, I rarely need to use Trip 'Em Up if there is a Black Orc using a Great-weapon attacking the same target. I receive buffs f Aion the abilities he's using in his Build stages whilst he's benefiting f Aion the separate ones I'm using as I rotate through the Build stages.
In summing up a conclusion, I belief Black Orc has a mechanic forcing it to diversify and this has benefitted it.