Fire of Exalted Wisdom
The fire Zuko and Aang get given from the Chief symbolizes wisdom.
Remember Roku’s statue in the first season? The decorative flames behind him are called “Flames/fire of exalted wisdom”.
If you compare the flame filled door/alcove behind the Chief with the flames on Roku’s statue you will notice that they are similar in shape. Both share the tear-drop shape and the multiple layers, implying that, since they are from the same nation, they also share the same fundamental idea: wisdom.
Which makes sense in the greater scheme too: Zuko and Aang carry the flame of wisdom to the dragons, who then grand them wisdom (the true nature of firebending) by engulfing them in flames aka wisdom.
Image source: One