"Subduing The Two Flames"
Either Blaze had a suitable medium that could mediate the two different elements, or made the two elements voluntarily join hands to balance themselves.
That's the two most common ways to balance Yin and Yang energy.
The second method was only useful for elements with self-consciousness, but it was almost impossible for two consciousness elements to voluntarily join hands with their nemesis.
Even if it was for the sake of their 'master', they rarely wanted to give up the natural feud between the two elements!
The two flames had not been with Blaze for a long time, which means, their loyalty was not high and it was even more impossible for them to stop fighting for the sake of Blaze.
The two flames could care less whether their master died or not. After all, in front of their nemesis, their lives were also at stake!