From The Big Fat Book of Magicalia: Edition 4- Higher Beings/Councils

Phoenixes are powerful, immortal shape-shifters (see The Big Fat Book of Magicalia: Edition 1- General, Chapter 64) who have remarkable magical capabilities, especially concerning pyromancy. They are most commonly seen as flaming birds. They are a self-created species.

Phoenixes are unlike ordinary shape-shifters in that they can wield magic like a witch. They are also capable of powerful shifts. When a shape-shifter is deemed worthy of becoming a Phoenix, the Flame Council, which contains all known Phoenixes, save one, will converge and create a pocket dimension. They will then be asked to shift into the most powerful creature they can. If this satisfies their requirements, they will become a Phoenix after the Ponovno rođenje vatre, or 'Rebirth of Fire,' in which the new Phoenix is rebirthed. 

Phoenixes are incredibly resilient to the elements and tend to be warmer to the touch than most ordinary humans. They also become essentially immortal, being rebirthed in the ashes of their body unless the ashes are cursed or the Phoenix is bound to their planet for one reason or another. In these cases, the Phoenix becomes a powerful spirit until their circumstances are changed. There have been no documented instances in which a Phoenix is truly killed. Additionally, they all have a telepathic link with one another and can teleport to any one Phoenix's location to provide support should one be in trouble. Their flames are as hot as hellfire and exhibit many of the same properties. Their flames are also capable of healing many wounds, and in the case of desperation, of necromancy should the body be dead for less than an hour. 

Phoenixes, while not nearly as powerful as a trained witch of similar age, have very powerful magic. They share many of the same strengths casting spells as naturally born elementalists.

Phoenixes do tend to run in families, although that is likely the shape-shifter gene rather than any actual Phoenix gene.