Weight vests are nice, especially for functional strength-training athletes. The thing about them though, except for the price because they can be expensive even used, is that you need to be concerned with your joints, primarily your knees. The impact of you walking around with much more weight on you than your body is used to can severly, negatively affect your knees. One way of going about that is to use it at shorter distances and work your way up, until your body has built the strength necessary to tote it around. But I think if you are aware of this potential problem and tread smoothly you should not encounter it.
How many extra calories will it burn? I'm not really sure. Weight vests are primarily used on body weight exercises, as the above poster stated.
To be honest, it might just help burn a little extra just for the way it will affect your breathing (wearing a vest is like wearing a trash bag sweater, but heavier) If walking is your main means of fitness then adding a vest and or light dumbbells and incorporating complex movements is of course better for results than walking without it.