IIRC, there's been several threads on this in the past. As someone who owns a business and pays sales tax collected every quarter, I don't see how an FFL can figure that into the tax form he must fill out, to calculate his payment due. Sales tax due is calculated on the percentage (in his location) of his sales revenue. For example, for me it's 5.5%. Certain counties also have a stadium tax, mine doesn't. It's not the FFL's sale (no revenue taken in) so how does that fit in the calculation? It doesn't. Other than his transfer fee, his sales revenue on this transaction is ZERO, therefore other than his transfer fee, any sales tax collected by him from you on this transaction would also be ZERO.... except any tax due on the transfer fee.
Personally, I wouldn't pay an FFL sales tax on anything other than his transfer fee... unless HE sent the payment to the seller. If he sent payment and I must then pay him, then he bought the gun, and is in turn, re-selling it to me and sales tax is due.