Cut the ends from the limes and quarter them. Place them into a food processor or blender with the water. Blend on a medium high speed for just a few seconds. Strain out the solids and return the liquid to a rinsed food processor/blender bowl.
Add the condensed milk, salt and rum if using. Add some ice cubes if desired. Blend on a high speed until combined and frothy.
Place equal amounts of pink salt flakes and white sugar onto a flat plate. Finely zest a lime on top and stir together. Squeeze the zested lime and place the juice into a bowl. Dip your intended serving glasses into the lime juice, then salt mixture to rim the glasses. Serve the limeade immediately in prepared glasses.