What is the best way to clean river rock stones in your flower bed?

I'd recommend Wet and Forget, you'd need to project the plants from overspray, but it's great for keeping 'the green' at bay for a long time.

power wash them

The green might be moss or even algae if the stones keep too much moisture. A picture would have helped. They are more difficult to remove, but they make the stones look established in the garden. :) The dirt can be washed off with the hose, when watering the flowers, just make sure the water falls onto the rocks to wash them, rather than on the dirt next to them (which splashes the rocks with dirt).

Green sounds like moss - you can buy a commercial moss killer to spray on the stones.

How can I clean my 2 to 4 inch river rock in flower beds dull looking

I soak them. Have an old cat litter bucket that I fill with water, dawn and bleach. Then put the rocks in that and let it sit at least a day depending on how bad the slime it. Good luck!