Yes, it is possible to flush the transmission.
And, it is possible to do incredible damage to a transmission by flushing it, rather than changing the fluid.
All too often, mechanics interested in a fast buck will flush a transmission without first changing the trans filter. This approach is likely to force debris from the filter back into the transmission, causing damage. The best approach is to drop the trans pan, clean it out, install a new filter and pan gasket, and refill with fresh fluid. If your mechanic insists on doing only a flush, then you must insist on a new trans filter before he does the flush.
Incidentally, if you are contemplating a flush because the transmission is acting up, it is probably too late to save it. The fluid and filter should be changed every 3 yrs/30k miles in order to prevent problems.