With the heater core yes the flush will help on the hoses no. You could check and see how hot the heater hoses are when the car is at operating temperature. If very warm to the hand on one hose and not the other then the heater core may be plugged. Do you live in a very hard water area? If you do then do not use the tap water when adding coolant mix to the car for the minerals will clog the heater and radiator cores. Use distilled water in the antifreeze mix.
It may also be a collapsed hose as well that is restricting the flow of coolant.