You could try an antifungal like Lotrimin Ultra (not AF) cream, and Nizoral 1% shampoo to see if the chalky skin is seb derm induced by malassezia. Think of the problem as an allergy to this commensal fungus (which means it's part of the normal skin flora), where the very upper part of the skin (stratum corneum) becomes sticky from reacting to malassezia, and your skin cells don't flake off microscopically like they should. Instead they clump up. Adding a moisturizer makes the sticky skin biuts even more adherent. It's treable but not cureable, so find a routine that works and use it every day. You should see results in two-weeks, and then you have a positive differential diagnosis for a malassezia allergy-type condition.
If the diagnosis is positive for a malassezia allergy, you could then include the only oil that malassezia cannot metabolize, which is MCT oil, sold at many web stores and at Whole Foods. It has a carbon chain length of only C8 and C10. Pure MCT oil will be too greasy (therefore not aesthetic), but you could make a temporary emulsion with 20% MCT oil and 80% water, and then shake it up each time you use it, and spray it with a mister onto your face so you don't apply too much oil. It will help soften and remove the flakes, and it won't cause any harm like all other oils, but by itself it doesn't cure anything. Keep it in the frig or make small one-week batches because this simple emulsion has no preservatives. (The accepted rule is anytime you add water to have refrigerate or use in one week.) There's a commercial product very similar to this called CapriClear, which is much more expensive but it's a much better emulsion so it's more aesthetic.