How can I reach the chests in the Iron Keep without dying?

As you enter the front door guarded by two Alonne Knights after the bridge, immediately head right and then left, up a set of stairs. Another Alonne Knight will be there, kill him and you will see some vases. Rolling into these vases will give you immense fire resistance. The vases, in combination with Flash Sweat and Orange Burrs and Radiant (or better!) Lifegems and as much health points as you can and preferably the Smelter's Demon armour set will net you the items.