I am eminently qualified to answer this question as I am currently demolishing 600 square feet of saltillo which will result in an estimated 6 cubic yards of debris. I lived with saltillo for years and have restored and refinished it, and now, I no longer want anything to do with it. In my case, it is laid on a 2-inch mortar bed with thinset adhesive. Someone, didn’t want this stuff to go anywhere 😉
First, it sounds like your saltillo is pretty badly weather-damaged if it is spalling. If the tile is extremely damaged, your only recourse is replacement. The interior is very soft and permeable.
Saltillo tile must be sealed. If you can live with the appearance problems caused by existing flaking, you may seal the tiles using a waterproof penetrating sealer. I had great results using Roval Saltillo Sealer 1088. It won’t repair the damage, but leaves a great looking finish and prevents further water penetration and damage.
For preparation, you may as well use a pressure washer. That will remove algae and dirt from the tiles and mortar. Allow the tiles to fully dry before attempting to seal.