Well if you have swift cast and you're up vs 1 Boss then I'd prefer to use swift cast for FIII, BIII if my rotation gets interrupted for some reason. To get as fast as possible back into my rotation. Let's be honest casting one of those spells without AF III/UI III is a pain because the casting time is so long.
However I agree and disagree with double flare (For multiple mobs it is, not on bosses). It's superb damage but it takes some time to get back into your normal duration.
(Have AF III up) Fire II spam> Flare>Convert >Swift cast> Flare> transpose.
Get raging strikes and quelling strikes into it before you start everything. The only thing thats meh is that after transpose you might cast 2x blizzards or Blizzard III to get back to full MP. But casting those is a paaaaaaain, takes quite long to cast. And if you are unlucky with transpose you might get your MP regeneration from the new gained UI 3-4 seconds later than it appeared.

Damage or faster rotation ?