I'm trying to write a webnovel that involves mythical creatures. I want to include Dragons, Angels, and Demons, and the problematic Phoenixes.
The problem I am facing is that there is no corresponding word that means "of a phoenix", like how the other three have the terms "Draconic", "Angelic", and "Demonic". The first word that came to mind was "Phoenician", but an online search gave vague results.
Perhaps you should trust your instincts. If phoenician floats your fictional boat, who are we to say it is wrong?
Using phoenician to refer to phoenixes makes just as much sense as using it to refer to people from Phoenix, Arizona... and yet (capitals aside) people do just that, probably as it is intuitive, vaguely pleasing in its (old) Old World pretensions, and the meaning is abundantly clear from the context, much as it would be in yours.
While phoenician definitely isn't dictionary-correct, in a fictional context I think you could certainly argue for artistic licence, especially if the dictionary isn't yielding something suitable.
I can see the need for an in-world word for "pertaining to phoenixes" and phoenixlike would, quite obviously, mean something different.
Also, there might be an etymological basis for making the link between Phoenicia and phoenixes - they may well be cognates - not that etymology should really sway you one way or another. (See this question for further details.)
Also there are some really good suggestions for alternatives in the comments to your question (where tchrist has helpfully mined the OED for you) and in other answers.
But it's your decision: your world, your nomenclature.
As others mentioned, the term "Phoenician" already has a different meaning. I'm not aware of official words for "of the phoenix", but perhaps "Phoenic" could do as a made-up word. It has the same "ic" ending and draconic, angelic, etc.
You could go with phoenixlike
adjective
having a resemblance to a phoenix in the sense of re-emerging and beginning again
- They create productive, phoenixlike new ventures and initiatives
adverb
in a re-emerging and rejuvenated manner like that of a phoenix
- Nixon's potential rehabilitation rests and continues, phoenixlike, to grow
Some synonyms
everlasting; perpetual; eternal
or
unfading or undying
Phoenician refers specifically to
A member of a Semitic people inhabiting ancient Phoenicia and its colonies. The Phoenicians prospered from trade and manufacturing until the capital, Tyre, was sacked by Alexander the Great in 332 BC.
'Phoenician', while morphologically the logical adjectival version of 'phoenix' (they are etymologically related), does not evoke the bird at all in modern usage.
'Phoenician' will most likely only evoke the ancient Mediterranean civilization, possibly their language, or sometimes as a demonym for people from Phoenix, Arizona. Context would disambiguate these.
There are archaic/rare uses of 'phoenician' meaning bright red (like the bird) but the usual (still archaic/rare) term for that is
phoeniceous
(both can be found in the OED).
Since you are creating labels for an invented thing, I'd recommend not using 'phoenician' because that is so strongly associated with the people. Using 'phoeniceous' will force people to think about what it means, and everyone will realize what you are trying to do (avoid the adjective for the people) and understand it as the adjective form for the bird.
One may think that, since many animal types get their adjectives (bovine for cows, feline for cats, etc), that bird types would get similar treatment. And they do. This veers off more into culture because all those '-ine' words were actual neologisms that happened to catch on. Similar terms for bird types were invented (anserine for geese, corvine for crow) but for the most part those haven't really caught on outside scientific terminology. Except for maybe:
aquiline
which is metaphorical for the eagle's-beak shape of a nose.
Note that other birds get by with adding '-like': duck-like, goose-like, crow-like (if their scientific versions aren't available to you or your listeners). If you must follow this particular pattern, the word would be
phoenicine
but I personally find that infelicitous. 'Phoeniceous' feels better.
Depending on how creative, innovative or ironic you want to be in your novel you might consider using
Phoenicious or phenicious
although perhaps you run into problems with its generally accepted first meaning: "of a red color with a slight mixture of gray", see https://www.thefreedictionary.com/Phenicious.
A simple option is just to write, Phoenix. As in, a phoenix feather, which means the feather of a phoenix.
In many places just Phoenix, or phoenix’, or phoenixes’ (both of which would be pronounced phoenix’s in conversation), would serve the purpose just fine.
Depending on context [you don’t say, but I’m guessing you have phoenixes in mind as a “race”, with a full culture and civilization] you can often just use the noun, like say Phoenix culture or The Phoenix Navy.
I have no opinion on whether you should write phoenixes or phoenices.
Keeping the same pattern, so Phoenexic or Phoenixic, would work. Like Demonic or Angelic, if you put the emphasis on the second syllable, it sounds pretty good.
