There is no definitive answer from either medical or sports science experts as to whether walking in high heels burns more calories than walking in flat shoes. It's unlikely experts will advocate it because of the well-documented damage heels can do to feet and lower back. However, you can always determine for yourself how many calories you're burning.
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The Typical Walking Shoe
People who use walking as part of a weight-loss program generally wear flats for comfort and speed, but the number of calories burned should be roughly the same whatever type of shoes you wear. Wearing high heels may contribute more to shaping and toning the legs than burning extra calories, acting in a similar way to the range of fitness shoes developed to tone leg and buttock muscles.
Experiment and Innovation
You could test the concept by wearing an armband that measures calories burned. Experiment by walking the same distance at the same speed in sneakers or flats and then in high heels.