Here is a picture of a silk hood found in Coppergate, York, during the excavation there. It was, according to the museum's website, found in a 10th century pit. I'll let you make your own judgement on exactly how the cloth looks, but in my opinion it's recognisably shiny.

http://jorvik-viking-centre.co.uk/wp-content/uploads/2012/08/Silk-Cap.jpg

http://jorvik-viking-centre.co.uk/about-jorvik/gallery/

Here's another picture from the Yorkshire museum. Unfortunately I can't tell if it's a reproduction or whether the item was on loan.

http://i.imgur.com/M8ORg26.jpg

There's much more information about the excavation results in the York Archaeological Trust's book, "Anglo-Scandinavian Occupation at 16-22 Coppergate: Defining a Townscape."

BA in German and Scandinavian Studies here

Very little Viking clothing has survived from the period, especially in Iceland, as the volcanic soil is highly acidic and there for less than ideal for preservation. Furthermore, the sagas (transcribed oral history), which are our only primary source of information on the Vikings beyond accounts from other cultures who encountered them, are focused on people, their relationships, and events - they rarely delve into the aesthetics of the physical world the stories take place in.

TL/DR - Your best bet for finding information on Viking era silk is probably someone who studied period clothing in general, unless some hero can come up with a quote from the sagas about silk.

Here is a piece of Chinese silk (Tang-dynasty) found at Birka, the largest town in viking age Sweden and used from around 790 to 960AD. It's dated to around 618-700AD and most likely found its way here through Constantinople. Source

Here's another piece of textile found at Birka, although not Chinese. Click the image to enlarge.