OxiClean with the yellow lid or the white lid. I like the yellow lid and have whitened many things with it. Works best in hot water. You can presoak the jacket if you like and then wash, or just follow the directions on the tub. There is no chlorine in it. The white lid version has brighteners which might not look so great, I've never tried it.
Hydrogen peroxide should also work. Another old fashioned remedy is juice from real lemons, mixed with water and then the garment is allowed to sit in bright sunlight. Don't get the lemon juice on any metal parts of the garment.