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Flagstone isn't a good candidate for sealing. It is a shale rock which will continue to flake off due to the porosity of the stone
allowing moisture to flow through it from below. Sealing the top is superfluous.
As for cleaning, most likely, you are trying to get rid of mold and algae. A simple soap solution with bleach will work and then
scrub with a stiff bristle brush. Then was with a power washer, 40 degree tip and from a distance of at least 6" from the surface
to minimize flaking caused by the chisel effect of the pressure.