Burning Blood

Starting at 3rd level, your body erupts into ethereal flame while you rage which you can call into the material plane to wield against your foes. You have a pool of burn dice, which are d6s, equal to your proficiency bonus. While you're raging, when you hit a creature with a melee weapon attack, you can expend one burn die to deal fire damage equal to the amount rolled plus your proficiency bonus to the target, in addition to the weapon's damage. Additionally, as a reaction, when you are hit with an attack, you can expend one burn die to reduce the amount of damage taken equal to the amount rolled plus your proficiency bonus.

Soothing Fire

At 6th level, the fire that burns within provides succor to you. You gain resistance to fire damage, and whenever you expend a burn die you also heal for the amount you rolled.

Phoenix Dive

At 10th level, you tap into the essence of fire allowing you to traverse great distances upon fiery wings. As a bonus action, you can fly in a straight line towards a point you can see within 120 feet of you. Any creature along or below the flight path must make a Dexterity saving throw. A target takes fire damage equal to your Barbarian level on a failed save, or half as much on a successful one.

Once you use this feature, you can't use it again until you finish a long rest.

Embers of Renewal

At 14th level, you learn to harness the inferno allowing you to return from death with fiery vengeance.

While you're raging, when you are reduced to 0 hit points you can instead- without expending any- roll a number of burn die equal to your proficiency bonus instantly recovering hit points equal to the amount rolled plus your level in this class. Your revival also erupts in a gout of flame. Each creature of your choice within 10-feet of you must make a Dexterity saving throw. A target takes fire damage equal to half the amount rolled on a failed save, or half as much on a successful one. Your rage immediately ends.