First of all, I am not a cosmetic chemist, so take my remarks for what they are worth.
Because vinegar is mostly water, and because salt dissolves in water, that is what is happening. There is no "chemical reaction" as such.
You can add salt until no more will dissolve to make a supersaturated solution or a paste, if you like. You could add a nonsolvent to the vinegar to reduce the solubility, something like a glycol or glycerin. You may also find that a paste is likely to set up and become more of a cake than to remain fluid. If so, you would probably need other ingredients to maintain the thickness and flowability. To make it shelf stable, you would likely have to add other ingredients as well. You have not said whether you intend this for personal use or to be offered for sale.
If you are holding this out to the general public, you must take care, however, in using only ingredients that are generally regarded as safe (GRAS). In this regard, there are very few "secrets" in the personal care industry as all must stick with GRAS ingredients. Otherwise, the burden of proving that your compound is safe is on you, and you better have deep pockets to do the work and to settle the lawsuits. In short, if there is an existing product that is roughly what you are trying to do, then get it and find or figure out how it is made.
A quick look on-line for an apple cider vinegar salt scrub reveals these ingredients:
Sea Salt, Water/Aqua/Eau, Apple Cider Vinegar, Glyceryl Stearate, PEG-100 Stearate, Lauroyl/Myristoyl Methyl Glucamide, Coco- Betaine, Sodium Methyl Cocoyl Taurate, Glycerin, Persea Gratissima (Avocado) Oil, Linoleamidopropyl PG-Dimonium Chloride Phosphate Dimethicone, Rapeseedamidopropyl Ethyldimonium Ethosulfate, Aloe Barbadensis Leaf Juice, Quaternium-96, Dipropylene Glycol, Propanediol, Steareth-100, Steareth-2, Mannan, Xanthan Gum, Polyquaternium-70, Sodium Lactate, Sodium PCA, Glycine, Fructose, Urea, Niacinamide, Inositol, Hydroxypropyl Methylcellulose, Sodium Benzoate, Potassium Sorbate, Lactic Acid.
I would say owing to cost considerations that everything in this product is there for a reason, with the exceptions maybe of the avocado oil and aloe juice. You can look up each ingredient and try to learn what it is, and why it would have been included. Most products like this, would be fairly similar, and are distinguished by marketing lingo to differentiate and to attract customers, viz. words like: "avocado oil," "aloe," "apple cider vinegar," "pink Himalayan sea salt." This particular product is priced at $38/9 oz or over $67/lb, for something that is mostly salt (impure at that), water and vinegar. I note that the order of ingredients is usually taken as proportional to the amount contained, so it follows that salt is the main ingredient, and the ACV is diluted with water.
Hope this helps.
