Jasmine extract is (according to one supplier) a non-sensitizing and non-irritating flower extract. Recommended use level is 5%-10%. Lancome uses this ingredient in their Visionnaire line.
A Chinese study found that drinking jasmine tea can help prevent damage from free radicals, particularly on red blood cells. However, this refers to its use internally, not topically, as in a skincare product.
According to one skincare supplies manufacturer, jasmine “provides nourishing care to very dry and sensitive skin. It has a balancing and soothing effect and antibacterial and thus anti-inflammatory properties – for a harmonious complexion and for feeling comfortable in your skin.”
See also benzyl alcohol.
Sources
Allergy to Jasmine Is Not Always Delayed Contact Allergy
