What size?
If the silk is strong and in good condition, you could baste it to a piece of washed cotton fabric and stretch that, pulling just enough to make it flat.
If the silk is light-damaged and fragile, stretching might shatter the weave. In that case, I'd suggest a direct-contact mount using a padded, fabric covered substrate. The direct-contact overlay could be fine mesh silk Crepeline, polyester Stabiltex, Melinex 516, or clear acrylic.
The fine mesh fabrics usually are inconspicuous on textiles, but require careful assembly in order to create spring-tension between the overlay and the padded substrate. Melinex would be glossy and reflective, which could be a problem if it can't lay flat on the textile. The best choice for appearance and simplicity of assembly would be an acrylic overlay, especially optically coated acrylic, such as Museum Optium Acrylic.