Hi KatieP,
Welcome to the Mattress Forum! 
Mattresses sold in the United States are required to pass the 16 CFR 1632 and 1633 fire regulations with or without the use of fire retardant chemicals (the method of passing the regulations isn’t specified in the regulations). The most common method used by far to pass the regulations is the use of inherent fire barrier fabrics that are either quilted into the cover or are wrapped around the inner materials of the mattress like a sock. There is more information about fire retardant methods that are commonly used in the industry in post #2 here and in post #4 here. I’m not sure with which brands you were having difficulty finding out what they are using for their FR barrier, but most companies are transparent with this, as it is required by law.
They have to pass the 16 CFR 1632 and 1633 flame retardancy regulations for any mattress sold in the United States. What method they choose to pass this is up to them. From the information you provided (thank you!) they use the inherent fire barrier that is a rayon/viscose blend, which is the most common used in the industry, In a few of their mattresses, they use wool alone to pass the FR guidelines. The phosphorus based-inorganic salt they use is just for the plastic zipper area on the bottom of the mattress, if the mattress has a zipper. This is commonly used to control plastics turning into combustible volatiles.
Regarding testing the latex for harmful substances and VOCs, while Ikea lists no “safety standard” certifications for their latex on their web site, most latex produced would pass one of the different types of organic and safety certifications such as Oeko-tex, Eco-Institut, Greenguard Gold, C2C, and CertiPUR-US (see post #2 here), and I would generally consider it a more “safe” material.
Note that I’ve removed the photos of the IKEA booklet pages you’ve attached, as they were labelled “Internal Use Only”, I also removed the email you provided which had information for specific individuals listed.
Phoenix