According to the About.com laundry section, the best way to clean a polyester jacket is to machine wash it on the permanent-press setting: a warm water and a cool rinse setting. Wash the jacket using a high-quality laundry detergent; and, machine dry it using either the permanent-press setting or low heat. If the dryer does not offer a low-heat setting, hang and air dry the garment.
According to How Stuff Works, polyester clothing should always be turned inside-out before washing: This prevents obvious snags and other damage to the outside of the clothing. If the garment needs bleach, use chlorine bleach only. To brighten a white polyester jacket or any white polyester fabric, pre-treat it by soaking it in a solution of half detergent and half water, and then rinse it in white vinegar during the final rinse cycle.
Additionally, fabric softener reduces the amount of static on polyester clothes between washing and drying. Always avoid drying polyester on high heat, as this damages the fabric and causes shrinkage. How Stuff Works advises that if polyester garments require ironing, it is important to use a moderate-heat setting. Alternatively, use a steam press to minimize the chance of heat damage occurring.