Cleaning flagstone is a concern with many pads.
Most often the stone turns black because stone is very porous and absorbs all dirt and dust from the outside world.
When you have had enough of your nice looking stone turning black, the solution we use is Bio Klean from Prosoco.
There is a three part process to it. You need to mix the Bio Klean cleaner and activator together. You apply that to the surface, but you SHOULD ALWAYS APPLY IT TO A SMALL PART SO YOU KNOW WHAT THE RESULTS WILL LOOK LIKE.
After you are done with that, you will follow up with a Limestone and Masonry Afterwash.
The total instructions are at Prosoco. And feel free to call them. They have some of the friendliest customer service representatives that I've ever talked to. They can help with any masonry stain problems you might have.
Their number is 1-800-255-4255.
If you have mold or green on your stone, you can use Bio Wash. It is a much milder solution and it is easier to apply. That is also on their website.
Good luck with your cleaning!!