The only real worry with stainless steel is the potential formation of hexavalent chromium compounds. This is a major concern when welding stainless steel or when working with any alloy that contain chromium at or above its melting point. Unfortunately it's hard to find anything authoritative regarding the minimum temperatures required for such compounds to form, but I gather it's pretty dang high, probably well higher than the red-to-orange temps we hit dry-burning.
People dry-burn Kanthal all the time without giving it a second thought, right? Well guess what? Kanthal A1 has more chromium (over 20%) than 316 or even 430 stainless. Nichrome wire also has comparable amounts of chromium, yet it and Kanthal are used in all kinds of applications where they're hot enough to glow red and people breathe the air that's been in contact with 'em. Think toasters, hair dryers, and many electric heaters.