Sweep the flagstone's surface and then spray it with water from a garden hose, just enough to moisten the surface.
Apply a heavy duty coating stripper to the flagstone using either a paintbrush or a paint roller. Wait 20 minutes and check the old sealer to see if it is softening. Softening may not happen for up to 2 hours. Keep checking every 20 minutes.
Scrub the old sealer off with a deck brush. Get inside all the grout lines and stone crevices. Once the old finish is scrubbed off, rinse the flagstone with clean water.
Vacuum up any standing water with a Wet Vac. Allow the flagstone's surface to fully dry.
Apply a stone-penetrating sealer to the flagstone, following the manufacturer's directions. Use a paintbrush or paint roller to apply the sealer. Wait for the sealer to fully dry between coats. Apply two coats or more as directed by manufacturer.