This almost plays like a Rogue, but not quite. Using Flame Spike builds a combo point on your target. Engulf in Flames uses those combo points to apply a hefty DoT. The thing to note here is that more combo points doesn't increase the damage on Engulf in Flames, it only increases the duration of the DoT. The DoT also stacks, and the duration on the DoT refreshes when you add a new stack.
The goal here is not to use Engulf in Flames when you have 5 combo points, but rather put as many stacks of the debuff up as possible while making sure the duration is long enough that it won't immediately drop if you need to stop and heal yourself.
A 1-point Engulf in Flames will only stay up for 6 seconds. While 1-point finishers can stack the debuff very very quickly at the beginning of the fight, it won't work later. You'll have Energy problems and if you need to heal yourself, you'll lose your stack. When you're first learning how to do this quest, try starting by using 4 combo points, then the finisher. Another four combo points, then the finisher again. Repeat until you need to heal, or the other dragon is dead.
After you do that just fine a few times, move down to three combo points. You can keep a stack up with 2 combo points, but 3 is what you should stick with here. 2 is better for Malygos himself because you're not going to need to worry about healing at all, just using the Flame Shield at the right time. Stick with 3 or 4-point Engulfs on this quest.
You know how a Rogue can only build combo points on one target at a time? If he builds a combo point somewhere new, he loses those he had on a previous target? This works the same. Your enemy is a target, and you are a target. Building combo points on yourself via Revivify kills the combo points you had built up with Flame Spike. DPS or Heal, one at a time. Don't try to spam Flame Spike while building Revivify on yourself.
While doing Aces High! you generally don't need to keep your HP topped off. You don't need to be at 100% all of the time. Don't worry about being a little reckless, just keep stacking on Engulf until you're well below 50%. Once you do start healing, there are a couple of things to be aware of. First, your combo points from using Revivify stack on you, so when you try to use Life Burst, guess who you need to target? Right, you need to target yourself. Even if you have Auto Self-Cast turned on, you'll need to target yourself/your drake.
Unlike Engulf, Life Burst is something you'll probably want to use when you have a full 5 combo points. If not for the heal itself, more combo points will give you a longer duration on the Life Burst buff, which makes your HoTs more potent. Stronger HoTs means less time spent babysitting your health bar. If you're sitting in the danger zone, a 1-point Life Burst isn't a bad idea either, to get your HoTs up at full effectiveness immediately.