As far as I can tell, the zinc itself wouldn’t be particularly harmful (at least, not moreso than inhaling any other metal vapors). The nasty stuff would be manganese dioxide, which is a main component in zinc-carbon, zinc-chloride, and alkaline batteries. Generally, non-rechargable batteries won’t “explode” in a fire, but they will puncture and leak chemicals everywhere, which isn’t great. Lithium batteries, on the other hand, will absolutely explode and should be kept far away from anything that could damage them.