The incline treadmill for fat loss theory is very well studied and very commonly used by bodybuilders and fitness models. The ideology is to walk at a moderate pace on the full incline setting for a long period of time - approximately 50 minutes. This is to slightly raise your heat rate and put your body into an optimum fat burning state.
According to this theory, going at a faster pace on the treadmill (such as running) puts a greater demand on the body. This greater demand means your body needs a more immediate source of energy. When running your body prefers to use glucose as energy and if your glucose stores are low (which we often are when on a fat burning nutrition program) your body will try to break down muscle.
So how do I know how fast or how slow I should be going?
The easiest non-scientific method is to imagine having a conversation. You want to be able to talk properly with a few breaths in between each few words. You don't want to be struggling to get your sentences& out and you don't want to be able to talk as if you are sat down. "My day was very good *breath* today, how was your day *breath* today? (Not that we are encouraging socialising in the gym ;-) ).
Burning calories vs burning fat
Many people put up the argument about burning more calories when jogging/running or doing more intense exercise. Yes cardio at a hardcore rate for 50 minutes WILL burn more calories than a steady incline walk BUT according to this theory you will also be in a catabolic state - breaking down hard earned muscle for energy - instead of fat.
This is fine if your goal is simply to drop weight - but if you are on Aesthetic World you are most probably after maximum muscle mass and minimal body fat.
In a heart beat...
When it comes to burning fat it is all down to your heart rate. Keep it at a low level for a long period of time and you will put your body into an optimal fat burning state.