That's the standard opener in a nutshell, except that you'd preclude your first Flare with a swift cast, then triplecast Flare, Convert, Flare, Super Ether (or whatever Ether gives you 1200+ mana) Flare. It's not hard to work in that ether either; this is a BLM who doesn't use Sharpcast but I worked in the consumable because 4 flares is just GLORY. That's the only reason I even consider it. Fire 2 is useful if you have to revert to the old AOE rotation (waiting for CDs or Foul or whatever) instead of trying to creak out consecutive flares without Swiftcast/Triplecast. And if you're melded for spellspeed, T4 is so so good.
OP, here's some helpful tips for successful Black Mage-ing:
Get used to using Transpose to transition between Ice and Fire while you're moving between mobs. Your goal is to keep the timer active. This doesn't really do anything expressly useful until you get Foul at level 70 but it's a good habit to get into and it will help you regen mana between fights.
Also get used to starting your rotations with Blizzard 3. They changed the way Black Mage works a little in SB so until you hit level 60 and can make use of Blizz 4, Fire 4, and Enochian it's not really necessary but it'll make transitioning when you do have those skills much much more natural. Also you'll get used to the switch between B3 and F3. It's super fast and what you'll use instead of Transpose once you unlock both level 3 spells. And as Corbin pointed out, your damage rotation should always start with F3 so you have full Astral Fire stacks (3) to do damage in. You can extend your full stacks by throwing out a F1 but Transpose only gives you one stack no matter what so doing damage straight out of that is basically like poking something with a stick.
When you get Manaward, put it on your bar and keep it there. It's your tank stance.
And finally: the secret to Black Mage is that it's rotations are designed to make use of timing more than anything else. Your standard ARR aoe rotation is F3>F2>F2>F2>Flare>Transpose>F3>F2>F2>F2>Flare>Transpose X repeat (second part) ad infinitum (you can substitute an T2 for one of the F2s for the proc, I'd do it right after the Fire 3). This rotation is designed so that the slow cast of F3 gives you just enough mana for the 2-3 casts of F2 + Flare before Transpose starts the chain over again. The other rotations are like this also. Successful execution should make it so you never ever run out of mana. This is why BLM is a prime class to use the Manashift ability.
Freeze has always been the odd duck. No rotation I've ever used includes it but it's cool looking and useful for World Map so just keep that in mind. Happy Black Mageing!