Clean your outdoor flagstone walkway with soap and water. Walkways become dirty after use and exposure to the elements. Outdoor salt, chemicals, mud and other elements can stain the flagstone. Dish soap removes most stains. Wash the walkway every couple of months, or as needed, to keep it clean. According to cleaning-tips.net, outdoor flagstone walkways aren’t sealed, so they are vulnerable to weathering and more difficult to clean than indoor flagstone walkways.