Why is there no change in coolant level when adding coolant?

Maybe you have a air bubble in the system. Run the car for a while and it may clear out. If not you can idle the car on a hill with the front uphill to clear a air bubble.

To add to the above comment, do that with the radiator cap off. Google how to bleed air/burp a radiator.

Thank you. I will do that. However, I just flushed the cooling system. Should the air has been sucked out?

No, the air gets pushed out. Open the radiator cap and look down into the radiator. That tube you see is where the coolant gets pulled into lower radiator hose by the water pump. The coolant then flows back into the radiator from the upper radiator hose, flowing through the internal tubes of the radiator to refill the core around that tube you saw earlier. When the coolant fills up high enough it flows back into that tube to get sucked back in be the water pump. If you are bleeding air from the cooling system, take the radiator cap off, park the car facing uphill so the radiator is the highest point in the system. Run the engine, watching for when the coolant in the tube gets pulled in by the water pump, will take a few minutes as the thermostat open once engine reaches operating temperature. When that happens, make sure that coolant level doesn't go all the way down, or you'll just be sucking air back into system. Have new premixed coolant and a funnel ready to add coolant as it goes down. Any trapped air will come out of the little tubes (or ventrices) of the radiator, along with hot coolant coming back from engine. Once your sure all the air has been pushed out of the engine, you can top off coolant level and replace radiator cap. FYI, a cracked radiator cap can also interfere with radiator operation and overflow bottle, as it relies on vacuum to work.