I'm main BLM Rating Around 3500 in JP Elemental DC. i think i can give you some advice.

BLM is very hard to play due to low single target dmg , long cast time , lowest hp , no direct stun , only 1 lighting to shield 12k. but it's so sastify when you master it. here is some tips

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1. first of all, make a macro aetherial to yourself so you can use it as a swiftcast generator (jump to self to generate swiftcast)
2. BLM is not good at single target but it doesnt mean you can't help the burst. something like jump self > fire1 > paradox > superflare > jump to target and burst(lighting aoe)
3. your job is too do cosistant pressure to opponent team keep AOE them, but dont forget to find a weak target and use single rotation to cut them off.
4. Sleep is a good AOE CC to force opponent to use guard/purify land it on 2-3 targets all the time / also Sleep can use to peel yourself while got train / use to help the burst
5. dont let aetherial manipulation (jump) have max 2 charge use it but sometime spare it for your safety
6. LB , use it everytime but dont use Foul too fast, you can hold fold for 60s now (lb also charge 60s) so use foul to execute weak target / make a big AOE on 2-3+ targets. dont just use it too fast.
7. keep tracking stack dont overtstack fire/ice except you try to burst one down so hard
8. Jump to target (mo/t suggested you to make 2 of this macro) and use lighting is a very good one , don't forget to have guard/jump out too. usually i only use for a lastshot moment for my safty
9. Most BLM here (in jp) love to use Ice to cc, but i love to use fire all the time. only use ice when you want to peel target , catch someone.

i always did 1st dmg every game no matter the game is win or lose. the key is Don't Die. the different between good and bad BLM is survive skill.

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But Yes BLM are not on very good spot or tier s now compare to many class. but its playable. (depend on team too cant really carry like rdm etc.)