Besides the fact that we know that Davos is a returning POV in AFfC, Stannis’s use of the present tense when he says, "Lord Seaworth is a man of humble birth…" (III: 867) shows that Davos is alive. He is probably at Eastwatch, with the fleet and the royal household.
Alester Florent, who was condemned as a traitor, is almost certainly the man who was consigned to the flames (III: 856).
While in A Feast for Crows it’s stated that he is beheaded by Lord Manderly at the behest of Queen Cersei. Some believed that this must be some sort of trick on Lord Manderly’s part, which turned out to be the case in A Dance with Dragons.