Rub the spots off with a non abrasive plastic scrubbier or sweep to loosen and remove soil. Or fill a bucket of fresh water and 5 drops of dish wash liquid. Pour the solution on your Limestone tiles and scrub them. And add plenty of vinegar and scrub them with a non-abrasive sponge. Make sure you work in small sections because white vinegar discolors your grout line so work carefully. Do not use steel wool for scrubbing limestone tiles. After scrubbing, and before you move on to the next tile sprinkle some baking powder and scrubs with a sponge and rub the stains.
This is the method I use to clean my kitchen limestone tiles. It’s a very simple and useful method to remove streaks on your limestone tiles and retain their original shine. Instead of sprinkling baking powder you can prepare baking powder paste and apply them. Instead of baking powder you can also use bleaching powder. There are two types of bleaching solution for removing streaks and retain their original shine. Use oxygen based bleaching cleanser instead of chloride type. Add few drops after you wash your limestone tiles and scrub them and after 10 minutes rinse them with warm water.