The real answer.
Adventurer 1 takes a look ahead and seed 9 flames ahead of him. If there are an even amount of red flames, he says red. If there are an odd amount, he says green.
Adventurer 2 looks ahead. If adventurer 1 said red, indicating an even amount, and 2 sees an odd amount, he knows that his flame is red.
Adventurer 3 looks ahead. If 1 said red, 2 said red, he now knows there are an odd amount of red flames left. If he sees an even amount, he knows he is red. Do I need to explain this further?