One of the challenges of predators is getting to the thrips. Lady beetles and spiders will feed on thrips, but can get to them only when the thrips are on the move. Several ground predators will feed on thrips pupating in the soil. But during the stages when adults and larvae are feeding deep within the petals, tinier weapons are needed. The Six Spotted Thrips is a predatory species, but I haven't found it to be available commercially.
Thrips pose two difficulties regarding chemical controls.
First, their habit of hiding and feeding deep within flower buds reduces the effectiveness of contact insecticides. Second, thrips tend to develop resistance to insecticides under prolonged application. Horticultural oil and insecticidal soaps can be used on thrips moving from plant to soil, but have little effect on larvae and adults deep within the buds. However, they can be used to reduce populations before applying beneficial insects. Neem oil also has some effectiveness in reducing thrips populations.