Draconic Sorcery subclass:
Draconic Resilience: A strict improvement over the original, other than not getting it until level 3. Should generally give an extra +1 AC at level 4, and +2 at level 8, assuming you use those ASIs to improve Cha to 18 and 20 at those levels.
Elemental Affinity: The original had you choose an element at level 1, and then did nothing with it until level 6. Kinda pointless. This changes it so that you choose at level 6 when you get the resistance and damage bonus. You also don't have to spend a sorcery point to get the resistance bonus; it's permanent. Overall, strict upgrade, if minor.
Draconic Exhalation: This is gained at 10th level, where the original sorcerer did not get subclass abilities at 10th. It changes a single-target cantrip to a 15' cone, essentially making it a 1st level spell similar to Burning Hands. At level 11 (just 1 level after this is gained), Sorcerous Burst is 3d6 damage like Burning Hands, using exploding dice rather than half damage to make it overall similar.
While it may seem a little late to be getting a 1st level spell equivalent, it's using a cantrip, which means no spell slots are used. It doesn't have the range, but since it's a cantrip, you can use this while using Quickened Spell to cast another leveled spell. You won't use it all the time, but it should be a viable option fairly often. A decent enough feature.
Dragon Wings: While Sorcery Incarnate is active (1 minute of concentration, or 2 minutes if Extended), you can fly at your walking speed, and at the end of your turn do your Cha mod in damage to creatures within 15' of you.
This is decidedly mediocre. The original version allowed permanent flight at the same level. This version depends on a concentration spell that only lasts one minute, while the damage bonus only applies to creatures within 15' of you, and only at the end of your turn, when you can't move away afterwards.
This combines with the question of whether Sorcery Incarnate is worth casting in the first place. It requires concentration, so all other concentration spells are automatically excluded. Being able to use two metamagics at once is nice, but it's hard to imagine many cases where that would really benefit non-concentration spells.
As for advantage on spell attacks, that turns out to be incredibly limited. I can only find two spells higher than 1st level that make attack rolls — Scorching Ray (lvl 2) and Crown of Stars (lvl 7). There are several 1st level spells — Chaos Bolt, Chromatic Orb, Ice Knife, and Ray of Sickness — and of course various cantrips. Honestly, the cantrip Sorcerous Burst is probably the best spell to use to take advantage of that benefit.
In total, the best use of Sorcery Incarnate is probably to Quicken a leveled spell while using a second metamagic on it, and then using Empowered Sorcerous Burst as your action to gain the benefit of advantage on attack rolls. If you hover at 15' up, the cone effect of Draconic Exhalation and the wing flaps will both cover a 15'x15' square of ground directly below you.
Gaining flight to make use of that nova attempt while staying out of melee range is not a bad deal, even if the extra wing flap damage is questionable, but it depends on how much you buy into this approach.
Sorcery Incarnate being a spell that's intended to be combined with a subclass rider in order to really "manifest" your sorcerer's type (in this case, dragons) certainly makes sense thematically, but the implementation here feels weak. Perhaps if Dragon Wings made it so that casting Sorcery Incarnate gave you the flight speed and wing flap effects for 1 hour, rather than only being up for however long you could maintain concentration on the spell, it would be reasonable.
