Hi zagestone,
If you talk with Brooklyn Bedding / Dreamfoam they will provide you with the name of the manufacturer that makes their flame retardant barriers (I believe it’s Jones) so to the degree that Jones will disclose it you could call them and ask what was in it.
I agree with you that boric acid fire retardants are among the “safer” of the chemicals used in fire retardants (see post #2 here which compared the LD50 of one version of a boric acid flame retardant material to table salt).
Yes this is correct.
Phoenix