Welcome to the forum
@Chrysanthia!
The fire phoenix is one of the original phoenixes (fire/storm/aureate) and is - together with the original bears (brown/panda/polar) - always in rotation, as Herodite said
here:
So with regards to the Artifacts! As we all know the Original Bears (Brown, Panda, Polar) and the Original Phoenix (Fire, Storm, Aureate) Bases and Artifacts are ALWAYS in rotation! The base availability is of course subject to you not having one in either your City or Inventory.
Additionally, there are bases and artifacts for different evolvable buildings that appear in the crafter and spire on a 6 week rotation. Which ones exactly are announced
here. Please note: if the wording in that announcement thread is just as vague to you as it is to the rest of us, please refer to
this thread, which does a better job explaining how it actually works
However, like said before, the originals are always in rotation so should show up every now and then in your crafter recipes. The original phoenix artifact looks like this:
And, as
@PrinceHarry correctly said, there are also extra crafting recipes available during the Phoenix events (around Easter), with which you can 'trade' a new phoenix artifact for an older one in a 2:1 ratio. In addition to these crafting recipes, another thing to look out for are Tomes of the Phoenixes, which can also be gained during these Phoenix events as prizes. These tomes allow you to 'summon' artifacts for any of the phoenixes. One artifact per tome, so choose wisely
These tomes show up in your inventory under the tab Sorceries and look like this:
During the more recent Phoenix events, there were also crafting recipes that let you trade 2 new phoenix artifacts for 1 tome, so you can choose which one you want to summon. I'm not exactly sure if these crafting recipes have replaced the recipes that let you craft just the original artifact directly, but either way, both options will get you what you need
These crafting recipes look like this (example taken from the last Phoenix event's
wikipage):
So all in all it will take a bit of patience, time, artifacts, blueprints, tomes, blood and sweat to gather the base and all the artifacts, but I can assure you the Fire Phoenix is absolutely worth the effort!!