Is the speed of sound the fastest rate that a chemical reaction can progress through a substance? I read that a martensitic transformation can travel at the speed of sound in that material. Is that confirmed as being the fastest speed of a chemical reaction (transformation)?
Certainly, chemical reactions can propagate far faster than the speed of sound. If the reaction emits electromagnetic radiation, e.g. light, and is itself initiated by light, then the speed of propagation is the speed of light in that medium. See this article from Sandia National Labs, or from the Royal Society.