No easy way to flush the system fully.
About the only DIY path is to disconnect the return line from the trans cooler, stick it in a bucket and start the engine. Pour fluid into the transmission about as fast as it comes out untill what comes out is clean and bright red.
Essentially the same thing as formal flushing systems do. One possible snag, some transmissions use a thermostat to route only hot fluid to the cooler and if so, can thwart the effort by bypassing the cooler lines.
Still, worth the effort, water in the fluid can easily kill the transmission.
Not sure of the 4.0, but the 5.0 with the 4R70W includes a drain plug on the torque converter. Makes it pretty doable to all but fully drain the transmission, converter and cooler. From there, you can change the filter and while open, add a drain plug to the trans pan. A couple drains and re-fills should get the contaminates out.