As soon as possible, spray the mark liberally with hair-spray. Allow to sit for one minute then rinse in clear warm water. If some stain remains, repeat, until all stain is removed and then launder as usual. A friend of mine suggested this to me and it works great!
I've just tried it on my pricey raincoat made of 100% polyamide. It worked pretty good. I can barely see the stain now. Half way through, I started to spray on both sides of the fabric. The only drawback is that it had took me almost an hour to accomplish this.
Most people have a bottle of rubbing alcohol in their medicine cabinet and it is one of the best stain removers for ink. This is a page about removing permanent marker from clothing with isopropyl alcohol.
Although Sharpie markers are intended to be permanent, if you need to remove an accidental or intentional mark on a piece of clothing this page contains several suggestions including alcohol, nail polish remover, or a Magic Eraser. This is a page about how to remove Sharpie from clothing.
This is a page about how to remove permanent marker on polyurethane jacket. Permanent marker can be tough to remove, but here are a few options to try.
You may be able to remove permanent marker from your nylon jacket with the right products and process. This is a page about permanent marker stain on a nylon jacket.
Permanent marker is called that because it is difficult to remove. Once it has gotten onto clothing which is subsequently dried the task of removing it becomes more difficult, but not always impossible.