RE: Did I get the wrong battery?
Hi Ross,
The ElectriFly 1200mAh pack can only deliver about 6amps and your setup demands more. This is why your ESC is shutting off the motor.
Any of the cells suggested by Jason or Fred will work better as they have more current delivery capability than your 1200mAh cell.
You can either reduce your prop size to reduce the current demand within the 6amp limitation of your 1200mAh cell or choose a more appropriate cell for your power system.
Good luck!