Is the glue not sticking to the silk or the wood?
If it is not sticking to the silk it might be because of a sizing that is used on the silk from the manufacturer. You may need to wash the silk first. Also, with any cloth backings I like to totally saturate the cloth with water(sometimes with a mild detergent) and ring out the excess. This will allow the cloth to accept the water based glue.
Any carpenter's type glue will work...TB, TBII, TBIII, Elmer's, etc.