Some fabrics that have high ignition rates and are inherently flame-retardant are Kevlar, Nomex, spider silk, polyester, nylon, and cotton. However, unlike Kevlar, wool has a higher ignition temperature.
Then, the polyester is much more likely to ignite but will melt into the skin causing burns. This is why wool is one of the most useful natural fabrics in the world.
So, to answer the question, is wool flammable? The answer is that wool can only burn under very extreme conditions. However, it will also likely self-extinguish before causing much damage. So, wool is one of the fabrics that are fire-resistant and safe for you to use.