If you want to breed for a different nature, then don't bother. Mild works perfectly fine.
Mild is +Special Attack, -Defense.
And in Fire Red, all Fire type moves are Specially based, so they all gain a boost. Unfortunately, its Flying moves don't get the boost.
Then again, all Rock type moves are Physical, so any Rock move will hurt a lot, with the 4x damage and the 10% defense drop (approximately, at level 100). This is just the way attacks were categorized until Gen 4.
In-game, Charizard is a fearsome sweeper that can often KO opponents before taking much damage due to high Special attack, powerful moves, good speed and poor AI. And, in general, nature doesn't affect the utility all that much, because the level difference is generally enough to overpower your opponent. On in rare cases with a shoddy nature that lowers attacking prowess to help in some defense you don't need is it advisable to breed for a different nature or soft reset. Since Charizard is an offensive Pokemon anyway, the boost in its offense in exchange for defense is not that big a deal; it's not meant to take hits in the first place. If a strong opponent that you cannot knock out first is in in the first place, it's better to switch out to a defensive Pokemon, eat a hit, wear it down a bit till it's in range of Zard. In most cases. With that in mind, I suggest leaving it as is.