A flush service entails hooking up a machine which takes new fluid and forces it through one transmission line and then through the transmission and back out the other trans line. Trans fluid is not only a lubricant but also has conditioners and cleaners.
Think of a small babbling brook, that twists and turns down a gentle hill side. There are small sand bars and pools with still water interspersed. There are birds singing and a frog living on the bank. On the horizon comes a great storm, which causes the silt and sand to be deposited where it is usually not. The brook has been reshaped how sad.
So in the process of flushing, the normal build up of clutch and metal debris (think still pools with sediment) can break loose and move into the heart of the transmission (valve body) and then cause all types of mayhem.
Do not Flush a Transmission! If a shop offers or recommends this, see if there is any fine print which indemnifies them from any responsibilities should there be an issue once the service is done. We have seen this happen many times over the years.