Going to the gun shop and paying for it while they fill out the paperwork screams felony straw purchase.
The 4473 does let you buy it as a gift, it's just not as easy as giving them the gift card.
However, if Mr. Brown buys the firearm with his own money to give to Mr. Black as a gift (with no service or tangible thing of value provided by Mr. Black), Mr. Brown is the actual transferee/buyer of the firearm and should answer "YES" to question 11.a. However, the transferor/seller may not transfer a firearm to any person he/she knows or has reasonable cause to believe is prohibited under 18 U.S.C. 922(g), (n) or (x).
If you know where you are going to buy it, just call the FFL and see what they recommend? I personally don’t see why paying for it while they do the transfer would scream straw purchase. Who cares where the money comes from, whether or not the transferee is allowed to possess the gun is the main issues of a straw purchase, right? I would opt for that over a gift card.
Or maybe buy it yourself and then do an e-transfer after gifting?