If you can keep the flame on the melting nylon, it smells like burning plastic. Polyester is a polymer produced from coal, air, water, and petroleum products. Polyester melts and burns at the same time, the melting, burning ash can bond quickly to any surface it drips on including skin. The smoke from polyester is black with a sweetish smell. The extinguished ash is hard.
Rayon is a regenerated cellulose fiber which is almost pure cellulose.
Rayon burns rapidly and leaves only a slight ash. The burning smell is close to burning leaves. Blends consist of two or more fibers and, ideally, are supposed to take on the characteristics of each fiber in the blend. The burning test can be used but the fabric content will be an assumption.