Nah, you can take a blowtorch to a modern mattress and you'll burn a hole through it, but it won't catch fire and spread at all.
In fact, that's literally how they test the flame retardant abilities of a mattress; it has to withstand at least 70 seconds of a blowtorch from a foot away. If the fire spreads, it's a fail. That's how most mattresses are tested under the 16 CFR 1640 standard.