"burn" is also a figurative term. They could easily have used another term like "drain" or whatnot. Doesn't Vin talk of the metals inside her as "reservoirs"? (I'm thinking of the part where Sazed gave her feruchemical store to swallow.)
In
Final Empire, I remember when Kelsier gave a vial of metals to Vin for the first time, and she swallowed them, she described it as feeling a reservoir of power that seemed to awaken within herself, or something like that. I don't remember if Kelsier or any of the other more experienced Allomancers have ever described how they "burn metals" but its just something that they simply do. That is why I asked the question wondering if there were any answers or theories about just actually how do the Allomancers burn metals.
I am also curious to know if the metals even need to be in the stomach. Could they technically still be in your mouth. How about the bloodstream
So far, I only remember an Allomancer burning or using the metals if they were already in their stomach, not simply in the mouth or bloostream. Thats why, in my opinion, they drink down the metal beads in a vial of water or another type of liquid, so that the metal can quickly get down into the stomach. But this brings up another question of mine.
After drinking a vial of metals, how quickly do the metals travel down the throat and into a body's stomach so that they can be "burned" or as Ookla also suggested, "drained."