The flame he sees and feels upon his resurrection is the ultimate fate of the wicked: being burned up'destroyed'in Gehenna fire, the Lake of Fire (Revelation 20:14-15). The Lake of Fire represents the second death from which there is no return to life. This death is final and permanent; it is the absence of life for all eternity. It is eternal punishment, not eternal punishing.
When the rich man opens his eyes in the resurrection, he sees the flame of fire that is about to destroy him permanently, and it paralyzes him with terror, making his mouth go dry. He complains that the flame is tormenting him. In these verses, the Greek word translated "tormented," odunomai, means "to cause pain; to pain, distress; pain of body, but also pain of mind, grief, distress." This rich man, resurrected to physical life, sees this Lake of Fire and realizes the terrible doom he is about to face. Sobbing, he suffers mental anguish and despair and begs for a little water from the tip of Lazarus' finger to cool his tongue. Nevertheless, he must reap what he sowed'death!
Martin G. Collins
Parable of Lazarus and the Rich Man (Part Two)