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 bead like residue
which crumbles easily with fingers, giving burnt hair smell

Cotton/Rayon: Burns continuously with paper burning smell, Rayon leaving white ash

Nylon/Polyster: Burns fast and melts like plastic, forming Polyester hard uncrushable beads.