Are you asking specifically for Feast? Or Frontlines? Or both?
I can't speak for BLM in Feast but in Frontlines BLM is very solid in my experience so far having leveled it from 30-48 solely in frontlines. The benefit to BLM is the burst and high chunks of HP you take out with each Fire IV/Flare/Foul. I leveled Machinist in frontlines from 30-60 and while they have good DPS, it's steady, consistent, and predictable DPS. Even if you run a burst combo using ammo and wildfire while overheated, it's still steady damage over a 10-15 second period. But BLM is able to drop big numbers quickly, and surprise kill some targets before healers have a chance to react.
I typically top the kill/damage charts as BLM in frontlines, and it's easier to pull off 300k+ damage with BLM than it is for Machinist. Though I put more focus on damaging ice as a Machinist since ices have a lot of magic resist for some reason. So as a BLM I'll try to snipe kills while an ice is up whereas on MCH I try to get as many ice points as possible.
It's been a learning curve but here's what I've found helps throwing big damage out as a BLM:
1) Bind an easy "target closest enemy" button. Many times you'll land a Fire IV and they run away or your target runs away mid-cast. Quickly changing targets to someone in range is key to constantly be tossing out big damage. If someone marks a target for burst then try to help with single target burst, otherwise the less you have to move, the more damage and kills you'll make, so find a safe spot in the back, target closest enemy, and Fire IV away.
2) Bind an easy button to Swiftcast. This lets you toss a Fire IV / Flare / Foul while on the chase OR follow up with Flare right after a Fire IV for some real huge and quick burst to catch a healer off guard.
3) Fire / Blizzard are instant casts when Astral Fire/Umbral Ice is up. Always try to be tossing free instant spells while you're moving or chasing.
Other tips: Don't forget you have Sleep. Sleeping healers is a great way to allow your teammates to secure kills. Sleep + Swiftcast is a great way to run away from Melee if you are caught out of position.
I haven't learned how to really utilize Thunder yet. Other than implementing it in my ice damage combo, I've struggled to use it well against other players. That may be an avenue I haven't explored to bring BLM to it's full potential.
I think my game-winning carry potential might be slightly better on MCH but now I'm trying to get the Hand of Mercy title and for that, BLM is performing very well for me.