Soap flakes are just grated bars of soap. They are basically shredded soap to make it easier to dissolve in water. Used in the form of flakes, it is a natural washing powder that is gentle on delicate fabrics (linen, wool, silk and baby clothes) and it helps avoid allergies and skin irritations.
Of all the recipes, this one has been the most difficult to formulate. I have tested dozens of procedures over the years: cutting lemons and trying to make a liquid detergent from them, mixing Castile soap and vinegar, shuffling different powders in all sorts of imaginative combinations, and so on.
I know that lot of people prefer not to use the softener, but it would be imperative to utilise it in the washing-machine, in fact, washed clothes are very alkaline, especially if you use laundry powder, and their pH is totally different from our skin pH.