The only real (published, peer reviewed) study the product website mentions is one done by Ohio State University a few years ago. The study included a small group of 35 women who were postmenopausal
(probably over 50) and obese and
had type 2 diabetes
If you are not all of the above 3
then you may not see any benefit. You can read the study published at the American Journal of Clinical Nutrition to learn more about why this group may have seen results from the safflower oil (has to do with the hormonal changes after menopause and the effect on insulin, etc).
Note that the study did not involve the SafSlim product, and the same quality and dosage of safflower oil used in the study can be purchased for much less than the SafSlim product. This is particularly important since they state that it can take at least 12 to 16 weeks to see results. A $29 bottle lasts two weeks.
You can also replace the cooking oil you normally use with safflower oil (not in addition to). Buy regular safflower oil, not the "high oleic" version. High oleic is high in monounsaturated fats and it will state High Oleic prominently on the label. You'll want the regular kind that is high in polyunsaturated fat, and the nutrition label should state about 7-11g polyunsaturated per tablespoon. Use this in your salad dressings or when you normally cook with oil. The study used an oil with 78% linoleic acid and regular safflower cooking oil contains about 70% so you'll need a smidgen more. To match the amount of linoleic acid in the study, you'll need 2 to 3 teaspoons of of regular oil. Try to go with an organic brand such as Spectrum.
SafSlim mentions on their site that they use a clinically tested ingredient, but they make it very vague that it wasn't their clinical study - they still refer to the OSU study. In fact, they don't have any of their own studies to back up the claim and state that the product was inspired by the OSU study. I noticed that the SafSlim domain was registered just a few days after the OSU study was published. Knowing how this industry works, I would guess that someone from a supplement company read the report and saw dollar signs. Registered the domain, whipped out a product and promoted the heck out of the OSU study - all the while failing to present the full facts of the study other than linking to a zip file that most people probably won't open. This is typically how it's done.
SafSlim mentions "patented technology" but what they have applied for a patent for (applied, not yet received) is an emulsion technique of blending oil and other ingredients.