I dont know of any places that do a transmission flush, whatever that is. Every machine that I have seen does an exchange of the fluid. The trans itself does the pumping and just takes in new fluid as the old fluid is taken out. Very smart thing to do as long as you do it somewhat regularly. Actually, that is the only way you are going to get all of the fluid changed out of the torque converter. You can also do this with a couple buckets and some extra line hooked up to your cooler lines. If the vehicle has a shit load of miles on it and the fluid is black and shitty already the new fluid may be too slippery and the trans may not like that. You may experience slipping just because the fluid is no longer loaded with clutch material and metal filings.
As far as the problem in the first post. Let it warm up a bit like everyone has said. Also go to
www.howstuffworks.com and see how a torque converter actually works, it will make a lot of sense why the vehicle feels bogged down.