Can I use Kerdi Board instead of Cement Board to thinset natural stone tile?
All cement products contain silicates, from the sand use in the cement. It won't be breathable unless you create dust by cutting or breaking the panels. 

That being said, I don't see instructions for using Kerdi Board for flooring in the Schluter product data. It could be there and I just missed it, but I'm not seeing it. Schluter is actually pretty good about replying to emails, so you could ask them to be sure.

Another option to look into would be Schluter Ditra, another product from Schluter that is intended for use with flooring.