The wind is crazy here this week. We're stuck between a high and low pressure system and the pressure gradient (always moves from higher pressure towards lower pressure) is zapping the moisture out of the trees, grass, soil... And skin and lips. I love it when meteorology and skin/hair care can be combined in one paragraph!
Windburn, sunburn, and dry air can make your lips dry, chapped, and peel.
To deal with flaking, peeling lips, brush them. If you have an extra-soft toothbrush, very gently brush your lips in small circles with a dry toothbrush. Firmer toothbrushes need to be moistened first.
You'll find your lips are softer and smooth and much easier to keep soft with just a little lip balm (avoid the very waxy kind) or skin lotion. Once per day is enough.
If you wear lipstick, this will make your color go on smoothly and not tend to dye the dead skin but wear off the healthy skin, leaving you with blotchy color.