Dense greases would be an option; but it would make the bird rather heavy and probably not be good in the air... if it can even still get up in the air.
You could utilize those proteins differently and have them form tiny crystals on the outer facing areas of the feathers/body. Using an efficient system of energy transduction via the crystalline geometry; you could slow the incoming energy (fire) down to a less agitated state, which would turn the fire into light/energy... this could then be dispersed throughout the crystalline network and put off a glow of some sort; if you cared about getting rid of the energy. -- the bird could also utilize the crystalline system to ingest the overly agitated energy (fire, or other energies)... slowing it down enough to direct it through the body.. similar to what trees do. (Rereading this, you could also utilize that same absorbed energy, or the birds own energy to constantly emit energy through the crystals at a frequency that made the air surrounding itself very cold (slow) [if using the birds own energy, you need no transduction and just emission].)
Remembering that heat is created by fast moving particles and cold is slow moving... playing with that basic rule, you could make for many variations in this.
You could also bring in trace minerals.. and the ability to utilize metals in the feathers/body.. creating conductivity and allowing for the energy to go places throughout the body.. or even projected outwards into the environment. This may cause a weight issue...but probably not.
---- It also depends on how long you want this creature to endure fire. A light grease could make it fireproof for flying/swooping through fire... but staying there too long will make it go up in flames.
If I were you I'd get into condensers and crystalline stuff... that'd make it quite easy to convey and be very magical while still believable. You could also work with skin and heat transfering, heart/heat pumps... lots of stuff possible when you think of the process as "heat exchange" instead of "fireproof".
-edit for specific phrasing to "answer" question- A naturally occurring substance would be a self produced cellular protein which can be utilized in the construction of the feathers, hairs or skin of the bird. This protein would be crystalline in nature. -- being that the question is looking for a natural substance that "could occur", this is perfectly possible. Probably similar to what Will mentioned with pyrophosphates.