When you diet, you'll typically be eating less fat. However, as soon as you lower your intake, your body will take steps to store it, thus making bodyfat loss more difficult. So flax basically replaces the "bad fats" that you're cutting down on, with "good" omega 3 fats, keeping your metabolism from slowing down in an attempt to store it. There's also the benefit as a replacement energy source from a calorie-lowered diet.
There's also quite a bit of anecdotal evidence of other benefits such as skin benefit, higher energy levels.....I think there might even be a thread somewhere listing all of them.