Flames currently drop from the Lava Monsters. It is used to craft the Diamond Protection, Amethyst Protection or Reidite Protection.
The simplest way to obtain this is to get as many Lava Monsters as you can, kite them over to the border of the winter/lava border. And hit them where they can't get you. Keep note that all weapons are weak against this except the reidite weapons.
You need 10 flames to make the diamond protection, 15 to make the amethyst protection and 25 flames to make the reidite protection.
The flame was added in the "It Smells Like Burning!" update.