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).

In AFfC, it’s stated that he is beheaded by Lord Manderly at the behest of Queen Cersei. Some believe that this must be some sort of trick on Lord Manderly’s part. Only the next book will be able to reveal the truth of it.