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The water heater never drains unless you shut the valve on the cold water line off and hook a hose onto the bottom of the tank. It's always full of water under pressure so flushing the toilet would have no impact on the water heater. I suspect the noise is coincidental to flushing the toilet not caused by flushing the toilet. The type of noise you describe is often happens when the burner or heating element comes on. Its caused by mineral build up or sediment build up in the bottom of the tank.
You can try flushing the tank. Here are instructions:Turn the water off to the tank and turn the gas valve to pilot. If this is an electric heater turn off the power to the heater. Then hook a hose onto the drain faucet at the base of the tank and open the drain. If no water comes out turn the water back on to the tank to get it going then shut it off again. Next open a hot water (only) sink faucet to let some air into the tank so it can drain. Once the tank is drained close the sink faucet you opened but leave the hose attached and the drain faucet open and turn the water back on full blast to the tank. Let it run for 5 to 10 minutes then close the drain and let the tank fill. Next open a hot water faucet and let it run until the air stops spitting then turn the gas (or power) back on