The special features for Godzilla: King of the Monsters indicate that Rodan may not have had fire powers prior to entering the volcano in Mexico. In Godzilla: King of the Monsters, Rodan, known as the "Fire Demon", was a powerful force of destruction, due in part to his burning wings and fire powers.
In the MonsterVerse sequel, Jonah (Charles Dance), Emma (Vera Farmiga), and their team of eco-terrorists set out to gradually release the 17 Titans on the planet in an effort to save the Earth from the damage caused by humanity. After unleashing King Ghidorah, Godzilla's ancient rival, Jonah's team uses the Orca to wake up Rodan, who has been quietly slumbering in a volcano in Isla de Mara, Mexico. Rodan's awakening leads to a brief battle with Monarch and, eventually, King Ghidorah. Rodan later gets a chance to use his fiery wings to mortally wound Mothra. At the end of the movie, Rodan is one of the Titans who bows down and accepts Godzilla as the new King of the Monsters.
One of the special features included on the home video release of Godzilla: King of the Monsters, titled "Reimagining Rodan", sheds some light on where Rodan's fire powers actually come from. According to director Mike Dougherty, Rodan's fire powers come as a direct result of hibernating inside a volcano. What happened to Rodan can be explained by basic science: when an animal species begins living under unfamiliar, unsuitable conditions, it adapts to its environment over a great deal of time. Rodan survived simply by adapting to the volcano. As time passed, Rodan grew an outer shell of volcanic rock.
This could also explain why lava circulates through Rodan's body as blood. It could have been another biological byproduct that Rodan experienced as his body adapted to living in volcanic conditions for many years. What all this suggests is that, prior to his resurrection, Rodan was not the Fire Demon at all. Instead, he could have been more like his Toho counterpart. Though Toho's Rodan did live in a volcano, he didn't typically possess fire powers or a volcanic outer shell, which is unique to Legendary Entertainment's MonsterVerse.
The idea that Rodan gained fire powers from the volcano begs the question: where did Rodan live before hibernating in the volcano? Along with Godzilla, he could have been a resident of the mysterious underwater civilization in Godzilla: King of the Monsters, since he, too, is depicted in one of the murals found under the ocean. There's no telling what the Titans' lives were like thousands of years ago when the world was different, but Rodan probably didn't have his fire powers at that time.