Originally introduced in Magic: the Gathering's "Lorwyn" setting (okay, there were a couple examples in the earlier "Ravnica" expansion, but they weren't really treated as a culture, just as weird creatures associated with one of the factions), the Flame-Kin are one of my favorite races, and I have plans to use them in a campaign I've been working on for months. Here's my first-blush attempt to create playable rules for them, using the two rules-sets that I'm familiar with (3.5 and 5E).
Note that while googling, I found a race called Flamekin on D&D wiki, but they appear to be unrelated to the Lorwyn species, and the quality of material on that wiki is inconsistent at best, so I won't be taking them into account at this time.
Basic species info (Source: https://magic.wizards.com/en/articles/archive/lorwyn-lore-2007-09-10):
Flamekin are intense, passionate elementals made of stone and flame. They are daredevils and adventurers. Their ability to turn their body's fires from cold to intensely hot makes them deadly enemies in battle. Flamekin are semi-nomadic, born out of a desire to explore new lands and experience life to the fullest. They are a much wiser race than one might expect, being adherents of the Path of Flame, a process of physical and spiritual self-discovery that revolves around the fires that constantly burn upon their bodies. The Path is very dangerous, and very few flamekin see ito the end, especially since that end involves a fiery death the likes of which is rarely seen.
Additional Flavor Info (original writing):
Flamekin have an outer shell made of a graphite-like carbon composite, slightly flexible but significantly tougher than humanoid skin. The top of their head is open, and there are orifices at most of their joints; flames leak continuously from all of these openings, although the flamekin can choose to avoid burning anything with these flames. The body of the flamekin contains a skeletal structure of igneous rock; the space between their carbon exterior and their stony "bones" is filled with a mystical substance that is semi-liquid in consistency, and may even be partially composed of electrical, but acts as if it were as solidly resilient as human muscle tissue. When the flamekin body suffers damage, the elemental forces which bind their volatile substances together are disrupted, and some of their "flesh" dissipates back into the Aether between the planes; when killed, the flamekin's bones and skin remain behind as a corpse, but their flame vanishes entirely, although it's rumored that some flamekin mystics can voluntarily detonate themselves at the point of death, allowing their lava-like substance to explode out of themselves and destroy their own killers.
Flamekin characters have +2 Charisma, +1 Constitution, and +1 Dexterity. They are immune to fire damage and have resistance to cold damage, but water affects them like acid. As a bonus action, they can either "burn hot" or "burn cold"; while burning hot, they automatically deal 1d4 fire damage to any individual who makes a bare-handed melee attack against them, or 1d6 fire damage per round to any creature which grapples or is grappled by them. A flamekin who burns hot while wearing any flammable items destroys them; for this reason, flamekin cultures devote considerable effort to creating metal, ceramic, or other flame-resistant equivalents to items which other races find useful. Flamekin who are interacting peacefully with other races, exploring potentially flammable enviroments, or the like can "burn cold" in order to avoid igniting their surroundings; when this is done, the flamekin gives off only slightly more body heat than an organic lifeform.
+1 Natural Armor
+2 Dexterity, -2 Wisdom. Flamekin are literally and metaphorially hot-headed, have no sense of smell or taste and very little of touch, and are often preoccupied with either their own emotions or with a monastic path they devote themselves to in order to control their raging passions.
Favored Class: Monk (or Wilder if Psionics is in use). The Flamekin culture is highly dedicated to the practice of self-discipline in order to restrain their literally-explosive tendencies.