It could help but it also could cause a transmission that getting ready to fail go a bit quicker. Fluid flush is actually more like a transfusion of fluid. It does a more compleat change of fluid more than a drain and refill does, but in your case assuming your car has higher miles on it you can expect there is some age and wear in the transmission. In my opinion if the transmission is slipping at all ...new slick fluid may allow it to slip even more. I like to reccomend fluid changes and flushes as a preventative maintenance measure to extend the life of a transmission...therefore those services should done early in the game not late when its too late. Best to see a transmission specilist to see what to do first.
It seems more like a hesitation in the shifting than a slipping. The engine does not revive up while it shift but a delay in shifting.
The is a 2002 Honda Accord Coupe, I don't know why it changed the date
It could be something other than the transmission. In your case the first step is identifing the problem. A road test driving your car would likely me tell if its indeed in the transmission or something else. Fuel and ignition issures can cause the engine to have a slight power loss that make the you feel like its the transmission shift. Flushing the transmission is still a gamble in my mind. Its best to try and deal with facts.