To do a tranny flush, you don't do it from underneath. The tranny really doesn't have a filter, only a strainer, so you shouldn't bother dropping the pan -- in fact, that only removes a portion of the fluid in the tranny, anyway.

To do a thorough flush of all the fluid, you only need to detach the upper of the two lines into the radiator -- put a hose on the radiator's exposed nipple, and run it into some gallon containers that you've collected. You'll want to flush about 18 to 20 quarts if this is the first time -- followup flushes, 20 or 30 K miles from now, you can get away with ~12 quarts.

This, btw, exchanges all the fluid in the tranny, including inside the torque converter -- but remember that you're not emptying all the fluid throughout the tranny simultaneously, so there's a dilution factor (diluting new fluid with old), which is why you have to use more fluid than the total capacity of the tranny. See below for details...

Run the engine for a minute or two, during which about 2 quarts (1/2 gallon) will flow out into the containers -- refill with 2 quarts down the dipstick tube. Repeat until you've exchanged the aforementioned amounts.

And really, this is so easy you can do it in a white shirt and tie. The hardest part will be disconnecting the upper line connection at the radiator -- use good quality flare-nut wrenches, and lots of PB-Blaster beforehand; and put antiseize on the threads for the next time.

Have fun.

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Dilutions:

# of quarts exchanged ....... % of old fluid remaining
after 12 quarts ........ 15% of the fluid is old fluid
after 14 quarts ........ 11% of the fluid is old fluid
after 20 quarts ........ ~4% of the fluid is old fluid
after 30 quarts ........ 0.8 of the fluid is old fluid

As you can see, there is diminishing returns for larger volumes of flushing.