Did you know that fustian is actually a thick cotton and flax (linen) woven fabric? I actually pride myself in knowing quite a bit about textiles, but I had never heard the word.
Pronounced something like fust-chien, the word is also synomous with bombast (which also can mean cotton wool blend or pompous, inflated speech or writing) and etymological sources place its first use in this context around 1590. In Rege-Rom of Georgette Heyer, her characters will use it as an expression of high-flown or affected writing or speech–basically b.s.
Although sources don’t dig into to why a term for cloth would translate into a term for b.s., I imagine it is related to one of two things (or possibly both).
1. The material is thick and generally of good quality. In the same way we may call a person’s behavior “silky” (smooth, suave, sometimes a little sleazy) they may be called fustian or bombast for assuming to be a cut above every other cloth.
2. The term “laying it on thick” would seem to apply itself very well to fustian. A thick cloak of fustian fabric is an excellent metaphor for a steady stream of claptrap.