Of course wood ash is caustic -- they used to make lye from it. Fly ash is also not something you want to mess with.

When I made tombstones I had to shake down the filters and remove the buckets of silica dust (this was ultra-fine, it flowed like a a liquid) collected. I disposed of it in accordance with the instructions at the time: I dumped it in the alley outside the shop. I have a suspicion that this wouldn't be permitted today....