Sweep the joints between the flagstones with a wire brush to remove any already loose mortar pieces from the surface.
Position the sharp end of a cold chisel in the joints between the flagstones where the mortar is weak or crumbling. Hold the chisel at a 45-degree angle and strike the end with a hammer to remove the weak mortar. Remove up to 1 inch of the mortar until you have hit solid mortar material.
Brush out the chipped mortar with the wire brush.
Integrate five parts lime, 10 parts washed sand and one part white Portland cement in a wheelbarrow positioned near the site, using a shovel. Slowly add batches of water to the dry materials while stirring with the shovel until you achieve a consistency similar to that of buttercream frosting.
Spray a light mist of water over the mortar joints until they are damp to the touch.
Scoop up the wet mortar with a pointed trowel and firmly pack it into the the joints between the flagstones in 1/4-inch layers. Let each layer of mortar dry for 15 minutes before applying the next layer. Stop applying the mortar once you have reached the level of the flagstones.