What does the Center position do in a Dragonfire army?

The Center is the army's aura hub. The dragon you put there spreads its aura to everyone (itself plus both flanks), not just to itself. It's by far the most important slot.

Who to put there:

• By default: a Champion, for the damage-taken reduction aura (the strongest one observed sits at −27.5% damage).
• If you want Initiative (striking first): a Warrior.
• In short burst fights: whichever dragon hits hardest raw.

Neglecting the Center is mistake number one: you throw away a free team multiplier. Always pick your Center for what it gives the OTHERS, not for its own damage.