When you say that you have disconnected the trans cooler line "at the cooler", I assume that you mean the connection at the radiator.

If this is so, then it should be the top connection as you look down into the engine compartment.

You will need a length of ~1 inch diam hose. You can get this at a hardware store. I found the clear plastic hose easy to find. You'll need ~3 feet in length.

You clamp this on the outside of the hex fitting on the radiator (the one with the internal thread for the flare fitting of the trans line) with a hose clamp and run the hose down to the underside of the car where you can drain the effluent ATF into a oil collection container. I would recommend having the car on jackstands in the front as you'll have to pump new ATF into the fill tube where the stubby dipstick goes in.

While you're down under there holding the hose to the container, have your helper start the car and let it idle. The trans pump will pump the ATF out of the radiator cooler until it starts to suck air (~2qts). Then you have the helper shut the car off. You pump in 2 qts and repeat until you get clean (reasonably clean) ATF. This will take 10 to 12 qts; have a case of ATF handy.

The pump can be obtained from your local Kragen type auto parts store.

After you finish all the flushing, you hold the brake while you go thru all the gears, pausing at each to pump ATF thru all the passages, then top up just the cold mark, checking several times with the stubby dipstick.