There are no means to put out the fire, so maybe he can attempt to circumvent the fire. Since he has survived on the island alone for so long, we can assume he has the basic tools for survival. In this case, an axe is all he needs.
Assume the island is circular (any shape can be considered). I have taken the liberty of drawing an image for our understanding. The orange star is the origin of the fire, and it moves westward in a growing almost circular arc (not necessarily circular, since the wind will force it to cover more area in the westward direction.) Assume the blue circle is our lonely man, who we will call Chuck Noland for the sake of this solution.
So Chuck can simply move and cut off the trees in a sector of the forest in a triangular fashion as shown by the white section between the dark green lines, with one end as close to the centre as possible. The fire will reach the westward side of the sector first and die out soon as there are no more trees in its path. Meanwhile, the fire will take some time to reach the other side of the sector, starting from the centre and moving upwards. While the westward side is on fire, Chuck can stand close to the eastward side until the fire burns out the trees on the westward side. Once the fire has died on the westward side, he can move towards the burnt part and then stay put till the fire burns out the trees on the eastward side.
So Chuck has evaded death by fire, but with no more trees to provide fruits nor any animals to hunt and no usable wood to build himself a raft either, it's only a matter of time before Chuck dies of starvation. A pitiable end after a brilliant escape.