16 CFR 1633 is the regulation relating to STANDARD FOR THE FLAMMABILITY (OPEN FLAME) OF MATTRESS SETS.
Regarding your question about a chemical-free mattress, I do not believe there are any exceptions. Below is a similar question.
Q: Will the flame retardant materials aggravate allergies or asthma in chemically-sensitive people?
A: The CPSC has concluded that there is no evidence to suggest that exposure to flame retardant materials used in some mattress components would contribute to or exacerbate allergies, asthma or multiple chemical-sensitivity in consumers.
The CPSC found that the flame retardant materials under consideration for use in mattresses to meet the new flammability standard are generally non-volatile, are not associated with fragrances or odors, and are not derived from biological materials.
Concerned consumers will be further reassured by the fact that the CPSC noted that in most cases, most flame retardant materials are used within the mattress itself. The CPSC stated that by using the materials either within the mattress or in a manner such that the materials are bonded to the fabric or other barrier components in an effective manner, consumer exposure to the materials and any attendant risk to such exposure would be minimized.
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