A flush is draining all the coolant out of the engine, heater core and radiator then flushing out the complete system with fresh water typically from a garden hose.
Debris accumulates in the engine, heater core, radiator and hoses, the flushing gets all of this out.
Suggest you go to the AutoZone website at
www.autozone.com. The have a self repair section that should cover the model and engine setup.
The engine block will have a drain plug(s) the website should show these.
If the site does not have Avalon, try the Camry with V6 engine !MZ-FE. This is the same engine as your car.
As you are taking out the radiator suggest you go a few steps further and remove the thermostat then replace the thermostat housing (and hose). This will allow the water from the hose to move at full flow through the engine. Put the garden hose inside the top radiator hose when flushing.
Put the heater on full heat to open the valve. If automatic climatic control do this before shut down the engine the last time you drive the car before working on it. If manual you can do this with engine off.
Once you put every thing back together (make sure you reinstall the block drain plug(s) and thermostat). Slowly fill the radiator with coolant. You can squeeze the upper and lower radiator hoses to get more air out and allow more coolant in.
You want to get as much coolant into the engine as possible to fill up the cylinder head coolant passages.
One good check is to try to put in as much as you drained out, although there will always be some air left in the system until it bleeds out as the engine runs. Being a quart short on filling is OK, but a gallon is too much.
Drain, clean and refill the overflow coolant tank. Add more coolant then required as the level will drop when the air is bleed out of the coolant system.
Once you gotten all the coolant you can in the system start the engine and let it heat up. If the coolant level lowers in the radiator add more. When the T-stat opens the coolant level will drop and more coolant will need to be added. Don't install the radiator cap doing this time, you don't want the system to pressurize when working on it.
If uncomfortable doing the complete flush, just remove and replace the radiator. Attempt to put as much coolant back in as drained out. Use the hose squeezing method to help purge the air.
The engine does NOT have a bleed valve to open to help do this.
There will still be air in the coolant system that bleeds out over a short time of driving. Watch the overflow tank as it will lower, add more coolant.