Nope, all bedding materials have to undergo the same testing for flame resistance. This includes sheets, blankets, pillow cases, etc. Without the aid of any sort of accelerant, the most that'll happen is you'll get some smoke and charred bits.
Now granted, more people these days are buying bedding materials from Amazon sellers that may not be complying with US laws on these fire standards, so the risk is a bit higher if you're buying online from sellers you don't know. Which is why I always encourage people to NOT buy their bedding materials on Amazon, and instead but directly from a retailer in the US.