Vanilla fires (normal fire and soul fire), use two different sprite animations to render. Let's call them sprite0 and sprite1.
They are both used to render the fire you see on entities, but sprite1 is the only one used to render the player's screen overlay.

The first thing you need is your own pair of fire animated sprites. They need to be animated PNGs with a .mcmeta file describing the order of each frame.
It's required to follow this format when naming your fire sprites:

fire_id_fire_0.png
fire_id_fire_0.png.mcmeta
fire_id_fire_1.png
fire_id_fire_1.png.mcmeta

(you should put your own custom Fire Id in the place of fire_id)
The following are the sprites used for soul fire, which set the example you should follow: soul_fire_sprites.zip

Once you have your own sprites, you need to put them under assets/mod_id/textures/block/ (mod_id should be your own Mod Id).

If you wish for your mod to be supported by Slim Fire, a texture pack to reduce the space taken up by the fire overlay, you can either:

• Open an issue here asking for support.
• Come chat on our Discord and open a support ticket selecting the tag for Slim Fire.

In both cases, you will need to provide your mod name and either a link to the source code or the fire sprites and fire source block JSON models.
We will take care of adding full support, even by creating the new lowered sprites!

If you add custom Fire enchantments, you also need to add translations for them.
Luckily, this is very simple, just put under assets/mod_id/lang/ a JSON file named en_us.json with the following entries:

{
  "enchantment.mod_id.fire_id_fire_aspect": "",
  "enchantment.mod_id.fire_id_flame": "",
  "enchantment.mod_id.fire_id_fire_aspect.desc": "",
  "enchantment.mod_id.fire_id_flame.desc": ""
}

and fill them with the name you wish the enchantments to display and a brief description of what the enchantment does.
Of course remember to change mod_id with your Mod Id and fire_id with your Fire Id.

The entries that end with desc are technically optional, but adding them is a good practice for compatibility with Enchantment Descriptions and similar mods.
If you wish to add more languages other than English, you can find a list of other language tags here.

Depending on the Fire Component, there are different required assets. These are not specific for Prometheus, rather it's the same kind of assets you need when registering blocks, items, and particles.
It's highly recommended to check out official documentation, like NeoForge one. Furthermore, unless your Fire Components are highly customized, you can safely copy Vanilla assets.