I have oily skin, but I bet this exfoliation routine might work for you, which my dermatologist recommended, since it is rather gentle: Try getting a sponge (I use Buf-Puf brand) in a gentle texture, or a regular texture but make sure you scrub very lightly so you don't irritate the skin. Use it with Cetaphil soap, or if you want a more moisturizing soap, Dove soap, to wash your face every night. The sponge helps keep the oil out of my pores and quickly clears up any patches of dry skin that I may develop. And of course you could try it every other day or so if you'd rather.
Also, if you make sure to use a moisturizer on your face daily, that can also help cut back on flakey skin. I do have dry skin on other areas of my body and keeping it moisturized is usually enough to keep dry skin away. My dermatologist recommended Cetaphil moisturizer for my face because it won't clog pores, but if you don't have any problems with acne there are probably a lot of other brands that will work well for you! I know the regular Cetaphil hand cream works great on my hands -- all of Cetaphil's products are designed for senstive skin so they don't have any perfumes and other ingredients that often irritate senstive skin, and it works better at keeping my dry skin away than a lot of other hand creams I've tried.