Researching a little into Stravinsky's 'The Firebird' suite, I read a bit of the backstory to the ballet. Basically, a man enters a forbidden domain which is filled with magical creatures. He sees the firebird and captures it. The Firebird then begs to be set free, and promises to grant him a wish if he will let her go. She fulfils her promise when the king finds the man illegally in his domain. That was a very rough, largely incorrect sketch of the story.
I remembered also that Fantasia 2000 has a piece of animation to part of 'The Firebird' suite. Although the animation focusses mostly on a Sprite, the Firebird makes an appearance as a personification of a fiery volcano. In that instance, the Firebird is drawn to look like Tolkien's Balrogs as illustrated by John Howe. This isn't really the approach I'm going for.
I've started to draw birds to get an idea of what I want. Below is a concept design of a phoenix by Ben Wootten. I believe it was a potential design for the phoenix in 'The Chronicles of Narnia: The Lion, The Witch and The Wardrobe'. I did a pencil drawing of his illustration to get me into a bird-drawing mood.
My next couple of birds are less anatomically correct. I actually like the splayed wings of the first one- it suggest fire to me. The second bird is more precisely drawn, but it has no sense of drama or action in it. I'll probably take elements from these two drawings to create the final bird in my poster.