Phase 1
During the normal phase of the fight, the main thing you need to cover with healing is 468147. This raid-wide damage will happen five times across every phase one you do and increase the damage by 25% every cast.
While the damage of the later casts is notably higher than the earlier ones, you can't freely send cooldowns on every late-phase cast of 468147 because shortly after the final one, the boss should transition into phase two where even more healing will be needed.
The earlier casts do very little damage, and can be covered by normal rotational healing if people aren't taking unnecessary damage from other sources. Plan your cooldowns around what you will need to survive phase two and from there fit them accordingly to help with phase one 468147s around that. An example of this would if you plan to lb ec to heal the second phase two around 4:30, you can use it to heal the fourth 468147 of the first phase one at around 1:30 and still have it up
Phase 2
The timings of your phasing can vary slightly depending on how your group uses the 460633s. Once the boss phases she will go into a 45s channel where she takes extra damage and constantly deals ticking aoe damage to the whole group. How long you remain in the pase depends on how well your dps manage the adds trying to 460173 it, but ideally you want to be there for the whole duration which means you need to heal all that damage. stasis is already your most powerful tool as Flameshaper but it gains an extra edge in situations like these where you can slightly stagger the two engulfs while storing it and then delay the release a bit more so it covers different portions of it instead of being all concentrated in a single point
After the cast is done the boss will return to phase one, and cycle between until you kill her.