First, i would like to mention that while there is a lot of healing to do here, this is a very mechanics and positioning heavy fight more than a high healing numbers fight. When all the raid is doing their work properly the damage isn't wildly high and its very predictable, this combined with the fact that five-healer strats are viable means you aren't really going for absurdly high healing numbers, and instead to properly cover the major pain spots and priority targets.
437620
The main raid-wide damage mechanic of the fight are the 437620s, they will happen three times before the boss goes into intermission and they are 30 seconds apart from each other. This timing plays perfectly into Flameshapers strengths and makes it the recomended build for this fight.
On the first 437620 of every set, you can start your stasis and cast db while standing away from the group and aiming at less than four people. You need to do this in order to guarantee you get one of the db buffs on yourself so you can better control your stasis release later on.
Once you have your stasis started and the db buff on yourself, the 437620 will start its pull-in and damage, at which point you will cast engulf on yourself twice to heal the raid with consume. You want to try to hit the second engulf at the tail end of the 437620 in order to give you enough time to release at the correct timing later on.
For the second 437620, once again before the pull you want to apply db in a way that guarantees it on yourself. Once the damage starts releasing your stasis will cast the two engulfs stored in it on yourself and heal the group. After this by the time the third 437620 happens both your engulf charges will be ready for you to heal that last one before going into intermission.
You can repeat this process for every set of 437620s which means you can always send two engulfs into every single 437620 while the raid is tightly stacked together and all of them taking damage.
437343
The second important part of the fight is healing the targets affected by 437343. Five targets between every set of 437620s will need high healing on them and the best way to cover this is lb. Chronowarden has a stronger lb than Flameshaper so if healing these people is your main objective of the fight then there is an argument to be made for swapping specs, but Flameshaper can still cover them decently enough.
You would want to pre-echo every person targeted and then ve right as the debuff is applied to cover from the initial spike of damage, and a bit after using sb into the lb for additional healing