Cotton is a plant fiber. When ignited it burns with a steady flame and smells like burning leaves. The ash left is easily crumbled. Small samples of burning cotton can be blown out as you would a candle. Linen is also a plant fiber but different from cotton in that the individual plant fibers which make up the yarn are long where cotton fibers are short.
Linen takes longer to ignite.
The fabric closest to the ash is very brittle. Linen is easily extinguished by blowing on it as you would a candle. Silk is a protein fiber and usually burns readily, not necessarily with a steady flame, and smells like burning hair. The ash is easily crumbled. Silk samples are not as easily extinguished as cotton or linen.