Every mile you walk burns about 100 calories. The farther you walk, the more calories you burn. So yes, you can still burn fat and lose weight with a good walking program. You can even do some interval training with your walking, by speeding up for short intervals and then slowing back down to your normal pace.
As to your knee pain while running, it can often be lessened with improvements in footwear, running technique and exercises to balance your lower extremities through stretching and strengthening. For example, tight calf muscles, hamstrings, IT bands, quads, hip rotators, flexors and adductors can cause alignment problems that are aggravated with the impact of running. Strengthening of your calf muscles, quads, hams and glutes will help absorb the impact of running so that your knee joints absorbs less shock. However, while these measures can help, they won’t necessarily eliminate pain with running, esp. if you have joint or cartilage damage.
Alternatives to running - Walking is a great exercise if done consistently. Adding nordic walking poles to your walk can increase your calorie burn by incorporating more muscle groups of the trunk and arms. At the same time the poles allow you to transfer some of your weight off of your knees and get a better stride.
Elliptical trainers, swimming and cycling allow you to get a good workout with little to no impact to your knees. You can also get a good workout by running or jogging in water with or without resistance bands with minimal impact to your joints. The deeper the water, the less the impact.
For strengthening, stair climbing whether up or down, and squats may bother your knees depending on the origin of pain. Using equipment like a total gym or an exercise ball can help you strengthen your legs as they let you perform a squat with some support.
Hope that helps. And of course, hydrate well and eat a healthy diet. Good luck.