Some suggestions - use a syringe, like those used for adding fork oil (Motion Pro) for adding the coolant. Turn on the key and let the pump run while you fill. The system will run and purge air as you go. Wait a few seconds as you add and get close to the top for the coolant level to drop. Do this a few times until it appears to stay full. Put the cap on and ride around the parking lot or the neighborhood. Usually this will purge the remainder of the air and you can top off the coolant. If the pump later seems noisy, it's cavitating a bit and you can add more coolant. None of this hurts the pump, it can basically run dry.
Empty the system holds 750ml. You won't add that much during a flush and fill.