Dip a scrub brush in a small bowl of vinegar.
Scrub the visible limescale buildup on the flagstone vigorously until it's gone or until you make no more progress removing it.
Wipe up the vinegar with a wet rag. If only a bit of the limescale remains, repeat steps 1 and 2. If a significant amount of limescale remains, move on to step 4.
Saturate a cloth in pickling vinegar or lime juice and place it over the limescale deposit for an hour.
Scrub away the limescale with a scrub brush dipped in the vinegar or lime juice.
Wipe or rinse the area clean. Repeat if necessary.