Several things can cause the combination of a layer of dry, flaky skin combined with oily skin. More often than not this is caused by using the wrong combination of skin-care products. An emollient, wipe-off cleanser, followed by a toner that is too emollient for your skin type, and then an unnecessarily emollient moisturizer can prevent the lower layer of skin from exfoliating, creating a thick, dry, flaky lower layer and a greasy layer on top.
Conversely, if you have oily skin, using a drying cleanser followed by a toner with irritating or drying ingredients, and then applying an emollient moisturizer can create the same condition. The drying toner and cleanser can cause the skin to be dry and flaky, while the emollient moisturizer adds to your own excess oil production, aggravating it and making the skin look both oily and dehydrated.
The condition of dry skin underneath and oily skin on top rarely requires additional skin-care products. Instead, taking a completely different approach and eliminating overly drying or overly emollient products can help a great deal.
It is also possible that the dry layer covered by an oily layer could be a result of psoriasis, rosacea, seborrhea, or eczema. See the chapters dealing with those special skin problems and consult a dermatologist for an exam, if necessary.