From my understanding, CLA doesn't reduce your body fat but it may help prevent you from gaining fat.
http://www.3fatchicks.com/cla-conjugated-linoleic-acid/
That references an old study but here is what it says:
Dr. Michael Pariza, who conducted research on CLA with the University of Wisconsin-Madison, reported in August 2000 to the American Chemical Society that “It doesn’t make a big fat cell get little. What it rather does is keep a little fat cell from getting big.”
Pariza’s research did not find weight loss in his group of 71 overweight people, but what he did find was that when the dieters stopped dieting, and gained back weight, those taking CLA “were more likely to gain muscle and not fat.” In a separate study conducted at Purdue University in Indiana, CLA was found to improve insulin levels in about two-thirds of diabetic patients, and moderately reduced the blood glucose level and triglyceride levels.