Have you tried Borax? Soak in warm water with the Borax overnight then wash in woolite.
Add dawn dish soap to the bleach we use this years ago for restaurant aprons
Try a solution of lemon juice, salt and water. Soak
I use oxi clean in warm water . Soak a couple hrs . Then wash with your detergent and a have a scoop of powder oxi clean and use vinegar in the rinse . It has even turned yellow items from bleach back to white . Try it you ll love it .
I have whitened things like scarves and doilies using baking soda and peroxide.
Soak it in oxyclean and warm water, rinse it well and then set it in the sun to dry. The sun will help bleach it naturally.
I really like Biz. It will really whiten everything quickly. It is sometimes hard to find so I buy it from Amazon
Hydrogen peroxide if oxi doesn't work. Can't beat good old sunshine.
Chlorine bleach should not be used on silk. Rather than whiten silk, it turns silk yellow.
Antique silk is ruined by bleach and laundry detergents. Also will degrade in sunlight and air drying. Silk laundry flakes, vinegar, and squeeze with towels while lying flat. Best bets.