CLA doesn't burn fat per say:
It really hasn't been proven to do anything more than any other EFA.
When these fats are taken with protein they will speed up your metabolic rate. Your body will use more energy just to consume the compound.
In theory CLA also causes the inividual fat cells to stop growing. If they can't grow they most likely will not multiply. I don't believe there is any absolute evidence of this BUT those who have used it certainly give it many praises.
I would recommend taking CLA with your evening meals.