Adding onto <PERSON>'s answer and expanding and making it weird cause that's what I do:
Immortal Jellyfish. A sea creature who, when it reaches a certain point in its life, reverts to a younger version of itself. This is not breeding, but the same genetically identical creature, turning back time to its "baby" form.
So, rather than self-impregnation, I would say that the explosion and subsequent egg are the bird's way of reverting to its youngest form, in a method to extend its lifespan. This explains that the bird is the same bird, genetically identical to its old self, and not a child of the previous bird. Semi-perfect rebirth.
What I'm thinking here is that the "burst into ashes" thing is just an exaggeration born of human storytelling. After all, if you saw a bird combust, and there was a lot of heat, and not much bird left, you would definitely say something like "it totally effing exploded into ashes dude!" to your friends. But rather, I would perhaps say that the actual combustion is an implosion, rather than an explosion. The bird appears to "die" and collapses inwards, compacting the energy it has stored into a hardened, fire-resistant egg.
All that above could be posited into a bird format, under the right circumstances.
But what if we wanted to really play with evolution?
Perhaps what we should be looking at is a sea creature who looks like a bird. Something genetically similar to a catfish or flying fish, with fins that act as wings and rudimentary lungs. Shining and beautiful scales could look like feathers. The creature can spend some time on land, otherwise how else did humans see it. In fact, the creature we call a Phoenix spends its "childhood" near water or within very shallow tidal pools.
The first life stage is that of the "egg". In reality, this is a shell surrounding a tadpole-like creature. The creature probably uses baby fins and legs to drag itself around the sand or the bottom of a tidal pool to eat tinier creatures or algae. It is heat-proof, fire-resistant, and looks fairly egg-like to a casual observer. 671
The shell acts as protection, ensuring that predators have to work pretty hard to get to the gooey tadpole in the middle.
The second life stage is that of the adult, who enters the ocean or river to gather in groups. These creatures have evolved to eat ocean-faring birds like cormorants, sea gulls, and other creatures, by leaping out of the water. They would have two large fins that act as wings and two "back legs" with which to hold onto their prey. They would also probably have a hard beak with which to attack and kill, though they could just as easily drown the birds they capture, but would still likely have a beak-like jaw to tear them apart to eat. Their shimmering yellow, gold, crimson, etc scales would be to attract mates, despite their "immortality" they would still need to replace the population who died due to predators, disease, or human intervention. Mating would involve "flying" or leaping, or even walking to a tidal pool, laying eggs, and having them fertilized. Then the eggs harden and transform into the child stage described above.
So we have a sea creature with flamboyant coloring, feather-like scales, broad fins, back legs, and a beak-like jaw with sharp teeth. All of these things already exist in the ocean creatures of our earth, so they are possible, and some creatures have several of these traits combined, so we know they don't necessarily cancel each other out, we just have to put our creature through the correct pathway to get it all of these items. A casual beachgoer might see a mother Phoenix leaping out of the water and "flying" her way to a tidal pool and mistake this creature for a sea bird rather than the sea creature it rightly is.
The third stage of life is the "elder" stage, in which the Phoenix prepares to "die". They will eat voraciously, collecting as much food as they can, storing the excess fat and material like a mammal might in preparation for hibernation. They will also linger closer to the shore in preparation to walk out of it and find a suitable location to be reborn. This is the stage at which they are most vulnerable to predators because they are full of food and easy to get to. The elders will come onto shore likely in a massive group to help stem the number of deaths by predators, find their way into tidal pools or other safe locations. Almost simultaneously they will combust, compressing their bodies inward. They will revert back to their first life stage, releasing a massive amount of heat in the process, probably rendering their outer scales into ashes or something that could be mistaken for ashes in the process. 445