Path of the Ancient Dragon

Some barbarian tribes learn to loose themselves to their frenzy and rage, while others seek to emulate beasts of the wild, enhancing their senses and heightening their natural skills and fighting prowess. A few others choose a different path. Barbarians who follow the Path of the Dragon seek to rival, and perhaps even surpass the creatures who they believe are the true apex predators of the land. The majestic and deadly, true embodiment of death from above. Dragons.

All barbarians harbor within them the rage that grants them superior strength, constitution, and speed. For barbarians who follow the Path of the Dragon, that rage is the fiery wrath of a red dragon, the bestial cold of a white dragon, or fury that in some way encapsulates the rage of dragons.
These barbarians often hail from tribes who revere dragonkind, or who themselves are servants of powerful dragons. Their zealousness for dragonkind is the seed of their power, from which their dragonlike rage stems.

The rituals to create warriors whose strength rivals that of the great wyrms have long been lost to the public knowledge.  Such ideas are only found in the depths of both minds and woods, far from where any ordinary man could ever reach.  Yet, those that walk the Path of the Dragon Slayer are far from ordinary.  Using magics created by long-forgotten dragons seeking to rid themselves of potential rivals, barbarians of the Path of the Dragon Slayer are able to burn the unburnable, strike the unstrikable, and slay the unslayable

Dragon Manifestation

When you reach 3rd level, you undergo an obscure supernatural rite, receiving occult knowledge handed down through generations by the tribe's shamanic elders. This elaborate ritual involves the consumption of blood from a young dragon, in a very specific manner, (ritual specifics may be fleshed out by DM and player). This ritual succeeds only if the dragon’s blood comes from a true dragon, which must be slain by your hand, (the young dragon is usually captured with help of the tribe and prepared for the testing ritual). Blood from any other type of dragonkin, such as a wyvern, results in the ritual's failure, as well as shame and potential injury or even death to the aspiring dragon barbarian.
At the ritual's culmination, the dragons' blood unites with your own blood, quickening within your veins and imparting on to you a fragment of the dragon's mighty essence. This blood merging presents itself differently on different barbarians. Some manifest scale-like patterns on their skin, while others grow elongated fangs, some may even develop talons or slight horn-like formations on their heads. This transformation forecasts just the beginning of the changes you will undergo as you begin to embody the raw power inherent to all dragon kind.
The barbarian may repeat this rite every time a dragon of a different kind (blue, gold, green, etc.), is slain by his hand, though it no longer needs to be vanquished in single combat. As your evolution continues, you are drawn to seek out and challenge dragons of different types and of greater age. Every success allows you to absorb and manifest a greater range of their formidable draconic abilities. You can now speak, read, and write Draconic. Additionally, you gain proficiency om intimidation checks.

You have learned to channel fury of your dragons during your rage to reinforce your body with their own scales.  Beginning at 3rd level, while you're raging, you gain +2 to your AC and resistance to your Dragon damage type.

Dragon's Breath

At 3rd level, you learn a degree of control over the draconic abilities you have assimilated from dragons you have bested and consumed in combat.
Whenever you enter a rage you may choose a Dragon-type whose blood you've consumed through the Blood of the Dragon ritual. During your rage, you may use a bonus action to manifest a semblance of the dragon's formidable breath weapon as shown on the list below. 

Breath weapon save DC = 8 + Constitution modifier + Proficiency modifier. 

• Black: Acid in a 5 by 30 ft. Line (Dexterity Save)
• Blue: Lightning in a 5 by 30 ft. Line (Dexterity Save)
• Brass: Fire in a 5 by 30 ft. Line (Dexterity Save)
• Bronze: Lightning in a 5 by 30 ft. Line (Dexterity Save)
• Copper: Acid in a 5 by 30 ft. Line (Dexterity Save)
• Gold: Fire in a 15 ft. Cone (Dexterity Save)
• Green: Poison in a 15 ft. Cone (Constitution Save)
• Red: Fire in a 15 ft. Cone (Dexterity Save)
• Silver: Cold in a 15 ft. Cone (Constitution Save)
• White: Cold in a 15 ft. Cone (Constitution Save)

You may only choose one known dragon type to embody per rage, and you may use its breath weapon once per rage. 
This breath weapon deals 2d6 damage on a failed save, and half as much on a successful one.
This damage increases by 1d6 when you reach 5th level (3d6), 11th level (4d6), and 17th level (5d6). 

• If you are of the Dragonborn race, your breath weapon damage increases by an additional 1d6, if the dragon type you choose during your rage is that of the same type as you.

Dragon's Remnants

Black, Copper Dragon

While you are raging, your strikes are empowered with acid. On each of your turns, the first time that you hit with a weapon attack, that attack deals extra acid damage equal to 1d6 + your barbarian level.

Blue, Bronze Dragon

While you are raging, your strikes are empowered with lightning. On each of your turns, the first time that you hit with a weapon attack, that attack deals extra lightning damage equal to 1d6 + your barbarian level.

Green Dragon

While you are raging, your strikes are empowered with poison. On each of your turns, the first time that you hit with a weapon attack, that attack deals extra poison damage equal to 1d6 + your barbarian level.

Red, Brass, Gold Dragon

While you are raging, your strikes are empowered with fire. On each of your turns, the first time that you hit with a weapon attack, that attack deals extra fire damage equal to 1d6 + your barbarian level.

White, Silver Dragon

While you are raging, your strikes are empowered with cold. On each of your turns, the first time that you hit with a weapon attack, that attack deals extra cold damage equal to 1d6 + your barbarian level.

Dragon's Aura

At 10th level, you learn to channel the legendary fear that all dragons instill on their prey.

• As an action, choose one creature that can see and hear you and is within 60 feet. That creature must make a Wisdom Saving Throw or be frightened until the end of your next turn. The DC = 8 + Charisma (Intimidation) Modifier + Proficiency bonus.
• On subsequent turns, you may use your bonus action to extend the duration of this effect until the end of your next turn.
• This effect ends if the creature ends it's turn more than 60 feet from you, or out of your line of sight.
• A creature who successfully saves against this ability may not be affected again by it for 24 hours.

Dragon's Aspect

By 10th level, your connection to the draconic essence within grants you uncanny awareness and presence in combat.

• Blind-sight: You gain blindsight to a range 30 ft. every time you enter a rage.
• Draconic Courage: You emit a variation of a dragon's frightful presence, palpable by those allied with you while you are in a rage, granting friendly creatures within 10 feet of you advantage on saving throws against being charmed or frightened

True Dragon

At 14th level, you reach the pinnacle of barbaric dragonhood. You become Death from Above, proving equally deadly in the air as you are in the ground.

• While Raging, you sprout a pair of large draconic wings from your back, granting you a fly speed equal to your normal movement speed.
• Once per rage you may also use a bonus action to make a wing attack to a target of your size or smaller, that is within 5 ft. You vigorously work your wings in an effort to buffet a target adjacent to you, who is your size or smaller, (smaller creatures save at a disadvantage).
• The target must make a Strength (athletics) saving throw or be pushed back 10 ft. away from you and knocked prone. If the target succeeds, it resists and nothing happens.
• DC = 8 + Constitution Modifier + Proficiency bonus.
• Additionally, while raging, you have advantage on saving throws against spells and other magical effects, and gain immunity to your chosen element.