The only thing I can figure it working for is:
2 metamagics = Quicken + 1 other metamagic
Attack advantage = the paired cantrip
So the only question is if there are any spells that you'd want to use a metamagic on while also quickening them.
Subtle is kind of silly when you're flying and glowing with magic. You pretty much threw subtlety out the window already.
A Careful Fireball? Careful/Heightened Cone of Cold? Maybe Twinning it the next turn? Or actually, maybe use it on higher-level spells, like, say, an 8th level Sunburst (where the blinding effect doesn't require concentration) or 7th level Finger of Death?
You're far more limited on higher level spell slots, so using Heightened on them could be worthwhile, and if you're trying to max nova, tossing in a cantrip as well (or cone breath, for Draconics) gives a boost.
Is 3 turns of extra cantrip power worth the sacrifice of a 5th level slot? Well, that could be 12d10 vs 1 target, or 12d6 (~15d6 with explodes) vs 2-3 targets. So, maybe? I'd probably want 4 turns before I felt it was really pulling its weight, but that implies you're using up all your level 6+ slots on doing this, so even then feels really hard to justify outside of The Final Boss.
I dunno. Including the wing flap damage, I could maybe see doing this as a max nova approach, but it still feels like a struggle to make it seem worthwhile. Maybe run some numbers on it?
I barely would know where to start on the numbers, but let's try it? The problem is, I don't neccesarily want to look at this for the subclass, because if we find the damage is worth it for the Dragon subclass, what do we do with the Shadow Sorcerer who doesn't get the damage boosts? I'd want to avoid a situation where we say "this is fine" now only to find out it is only fine for a specific build.
So, DMG says that a 5th level spell should be 8d6 if it hits multiple targets (yeah, the same as a 3rd level fireball) so let's roll with that. I've always heard the standard for an AOE is three targets, so that would be 28 x 3. I'll just assume all saves are 50%, which feels close enough to me. So, if I'm right about how to do this, 50% hits three targets for 28 and 50% hits three targets for 14 (half on a save) which is
.5x28x3 = 42
.5x14x3 = 21
Which is 63 average expected damage (this is less than the 28x3, so I feel like we are on the correct track) And already... this isn't looking good.
I'm going to use Firebolt, just because it is a good standard. At 9th and 10th level when we get this, firebolt does 2d10 or 11 average damage. Assuming 60% accuracy that is normally (over three turns)
.6x11x3 = 19.8 damage over three turns. (no crits for spells... right...)
Advantage, according to the Treantmonk videos, increases the accuracy to 84% which makes it
.84x11x3 = 27.72 over three turns.
Which, since Sorcery incarnate is a bonus action, we are really able to just look straight at the difference... which is 7.92... This isn't great. Even if I added the 5 damage from the wing burst, over three turns, and against three enemies, that is only +45. I guess if I added the +5 damage to each of the firebolts from the Draconic Sorcery?
.6x16x3 =28.8
.84x16x3 = 40.32
40.32-28.8 = 11.52+45 = 56.52... even with all the subclass bonuses, you still aren't hitting the same damage as a level 5 AOE after three rounds of Sorcery Incarnate advantage on cantrips. And most 5e fights tend to only last about 3 rounds, so if you NEED to get to round 4, you have a problem.
So, the only play that even might have a chance here is Sorcery Incarnate, then cantrip turn one. Quicken + Heighten an AOE then cantrip again... but at that point, why not just Heighten the AOE and cast it twice? Or Heighten the AOE then Quicken the Cantrip, which is perfectly legal to do.
And you mention spells like Sunburst, but you can't twin suburst (twin is limited to 5th level) so... really other than heighten and careful what do you do? And frankly... just pick one or the other and keep your 5th level spell slot for another big spell.
Edit: Probably should run the numbers for 11th level, since you are right there.
.6x16.5x3 = 29.7 non-draconic
.84x16.5x3 = 41.58
Difference of 11.88 damage.
.6x21.5x3 = 38.7
.84x21.5x3 = 54.18
Difference of 15.48 + 45 = 60.48... still lower than a single turn, single action for the 5th level AOE numbers.