The purity of silk can be easily ascertained by a simple Flame Test. Take out a few threads of the fabric and burn them from their ends. The threads burn differently for different fabrics as stated below.
Silk
Burns slowly leaving a black residue which crumbles easily with fingers, giving burnt hair smell
Cotton/Rayons
Burns continuously with paper burning smell, Rayon leaving white ash
Nylon/Polyester
Burns fast and melts like plastic, forming Polyester hard uncrushable beads
For a more comprehensive silk purity test, you can walk into one of the Consumer Silk Testing Centres. For a nominal testing fee, get your silk products tested for purity in minutes and get a test report.