Wearing: Forever 21 top (old) & Revlon Lip Butter in 085 Sugar Plum
1) treat & protect
First thing, I recommend to figure out what's causing your dry/chapped lips and to address that problem first. For most people I believe that it's a combination of dehydration & climate that lead to their dry lip problem, but there are other factors that can contribute or cause your problem. Symptom find has a list of the 10 most common causes of chapped lips that might be helpful.
Once you've addressed your problem, lips balms can provide some relief with my favorite is the eos smooth sphere lip balm, which comes in this absolutely adorable packaging, and actually has a good formulation that hydrates your lips. And of course, I also recommend the huge variety of lip balms that Burt's Bees offers. Avoid lip balms with the ingredient petrolatum in it because while petrolatum is good at preventing moisture-loss, it doesn't actually do anything to hydrate your lips. And remember your sunscreen! Your lips are also susceptible to getting sun burned so a lip balm with SPF (which, a lot of lip products already do) in it is also quite helpful.
Depending on your lipstick formulation, it may or may not cling to the dry portions of your lips. So I definitely recommend giving them a good scrub to remove as much of those flaky bits as you can. At the moment, I'm using the e.l.f. lip exfoliator for how convenient and inexpensive ($3) it is. I also know that LUSH has lip scrubs available, however for $10, I think that's a bit pricey for something that is so easily DIY-able.
3) know the product
Lip products are not all created equally. For chapped lips specifically, I can recommend some of these. The Revlon Lip Butters are fantastic for keeping your lips hydrated with some color. They offer a really wide range of color and are reasonably priced. I also quite like the Korres Lip Butter, which has better ingredients in them, but are slightly more expensive & don't come in a such a wide range of colors & are not as highly pigmented. The Almay color+care liquid lip balms are also quite excellent at keeping your lips hydrated, but the color doesn't last as long as the Revlon lip butter. And lastly, if you're looking for a lighter feeling lip stick that still gives some hydration, I recommend the Maybelline Color Whispers These also come in a good selection of colors and are lightweight. Avoid matte lipsticks if you can as those tend to be more drying than other lip products as well. Other than Korres I haven't really tried out any higher end lip products, but I've heard good things about the Clinique Chubby Stick Moisturizing Lip Color Balm in terms of keeping your lips hydrated.
In summation, treat the causes of your chapped lips, wear lip balm (and sunscreen) often, exfoliate to remove flaky skin, and look for tinted "lip butter" products to start with until your lips do get better.
Those are my tips, I hope they were at least a little helpful! What do you guys do to keep your lips looking their best?