If you have Kino's available and can dump enough light on the green screen, I don't see any problem. The goal with green: plenty of light, consistently lit, no spill from the greenscreen itself to the actor, and no spill from the green's lights back to the actor. (Maximize distance of talent from green, as much as possible.)
Otherwise, I think you are in great shape. The BMPCC is a capable camera, so if you nail exposure and focus, you shouldn't have any problems in post knocking out the green.