Eventually Mokou would win because Flan isn't as immortal as she is. Flan would destroy her and she would respawn shortly, never running out of her own fiery power. Flan could destroy the fire too, but she would get damaged without the ability to regenerate like Mokou.
Therefore, Mokou is the world's greatest hero in the unforeseen event of a berserk-Flandre mass-panic. Everyone clap if you trust Mokou!!!
Argnator, that's what happened in Shino's fight between Flandre and Mokou. Eventually Flandre was too frustrated and tired to keep on fighting and she just wanted to go home.
they make good playmates, mokou is immortal and spends all her time alone in the bamboo forest when keine is teaching, and flandre is also alone in a basement, but she's lonely...and crazy