You can make a caustic solution with caustic soda & water, or you can use Poultice, or for that matter you can make your own poultice with plaster of paris powder and Coleman liquid lighter fluid. If you do this after placing the solution on the stone allow it to dry until it is a powder and then brush off and clean the stone if necessary.
Whichever way you go I would test it first in an inconspicuous place to make sure it does not stain the flagstone! After a week of the stain not coming back, wait another week (just to make sure) and then seal the stone with an impregnating mineral based sealer. Think HYDREX!
http://www.defusco.com/tenax-impregnator-and-sealer-liter-p-2095.htmlMark