Hi Metasequoia,
Post #2 here and the topics it links to has much more information about mattresses and children and “safe” materials including a link to some general guidelines for children in post #2 here. It also includes a number of links to the better forum posts and topics about mattress and children as well which also include more information about many good options for children.
While the most common method of passing the fire regulations in the industry are inherently fire resistant fabrics that are either used as a “sock” around the materials in the mattress or are quilted to the mattress cover and don’t involve adding chemicals to the mattress or have harmful substances that can leach or migrate out of the material or produce VOC’s that are harmful … wool quilting is also a very popular way to pass the fire regulations for those that would prefer to avoid synthetic materials completely whether they are “safe” or not.
You would need to ask each manufacturer about this since it isn’t something that would happen as a matter of course unless it was needed for a specific bug infestation (such as bed bugs).
The better options or possibilities I’m aware of in the the Philadelphia/Wilmington/Trenton areas (subject to the quality/value guidelines here) are listed in post #4 here.
Your budget is probably be too low for most 6" - 8" 100% natural Dunlop options although there are certainly a few options in your budget range that would probably meet your “safety” and budget criteria if you are also open to mattresses that include other materials as well
Phoenix