Am I doing something wrong as BLM?

[Aikaal]

Starting rotation (Can use it when you have CDs up):

F3 > Raging Strikes > T2 > Potion > F1 > F1 > F1 > F1 (Use procs) > Swiftcast > Flare > Convert

Regular rotation

T2 > F3 > F1 (Til 300-400 mana) > B3 > T1/T2 (Depending how much mana left you have) > Scathe/B1* > F3 and repeat...

*If you have a slow first mana tick
> Scathe/B1 (Blizzard 1 if you don't have to more, Scathe if you need to move)

There's few tricks to up your DPS in LeviEx. T2 ANY possible target (Tail include! You will take some damage but you dot still hit) More Thunders = more procs.
When Spumes are up, I always save the rest of my mana to Flare the Spume next to Leviathan's head.

If you are caught in a bad position, use Aetherial Manipulation.

Try to save Swiftcast when Levi hits the boat to refresh Thunder 2 (I use Thunder 3 on swiftcast)

**EDIT

When spumes spawn, I make sure to cast F1 > T2 > T2 > F1 > T2 > T2 to gett my stacks. Having high numbers is pretty hard in LeviEx, there are a lot of down time but you have multiple occasions to abuse of Flare. Each time you have two targets close, you can Flare.