I've heard different feedback on flushes. I determined the outcome has alot to do with the type of flushing machine and the experience of the operator. With a flush, the filter typically does not get changed nor does the sediment get cleaned out of the pan. You'll need to specify if you want the filter changed.
As Rivman said, I usually just drop the pan, change filter and refill and that process is outlined in the manual and works well if the tranny has had the recommended change intervals. The drawback to this process is you don't get the fluid out of the converter, only what has drained back to the pan which might be about half the total capacity. Normally not a problem but if the fluid is really old and nasty is can be a problem.
You have a couple options if you are concerned about this. Drop the pan and change the filter and refill with new fluid. Then disconnect the tranny cooling return line from the radiator, put a piece of hose on it and directed it into a large pan. Start the car and have 8-10 quarts of fluid ready and start dumping it in at about the same rate as its being pumped out. Once it starts coming out looking like new fluid, shut the car off, reconnect the line and adjust to correct level. This process can be a little tricky as you might imagine but I have found it to be effective.
If you are concerned about the fluid left in the converter and don't want to try the above procedure, do the "drop pan-change filter" process and drive the car for a couple weeks. Then have the fluid in the pan pumped out through the dipstick tube and refill again. At this point you'll have "mostly" new fluid in there.
Fluid rated as meeting Dexron III specs is fine.