By all means do the flush with synthetic. Two good ones are Amsoil ATF and Mobil 1 ATF. Both replace Dextron III and will outperform dino by a lot. It's an easy DIY project. I've posted detailed instructions which I have appended here.

Changing S80 Transmission fluid.
Power flushing is a simple DIY job. I use synthetic Mobil-1 ATF or Amsoil. You will need up to 15 quarts.
Disconnect the upper cooling hose. Squeeze the plastic retainer tabs together, push the hose in to release the catches and wiggle, wiggle, pull, pull. Cover the hose end with a baggie.
Clamp 6 ft of clear plastic 1 inch ID hose (hardware store item) over the radiator fitting, and prepare to drain into gallon bottles or a calibrated bucket, so that you know when you have removed about 12 quarts. Idle the engine to pump out fluid. Shut off immediately when bubbles appear in the clear hose. Add two quarts down the dipstick hole using a tranny filler funnel and hose from auto supply or chain store. Repeat the pump/fill cycle. Somewhere in the middle of this you may run the shift thru D N R while idling to assist the clean out. Once you've removed 12 quarts, the fluid should start running clean shortly thereafter, at which point reinsert the cooling hose into the radiator.

Topping-off tip. I put a scratch on my dipstick exactly 4 inches from the bottom. This is where my fluid sits with the engine cold, off, and level. It is a very good approximation of where you should fill to. The owner's manual has the official level check procedure.