It's impossible to have no flying units at all, and if a phoenix is going to belong to a faction (not be neutral), it should definitely be a Light Elf unit (even though it's associated with fire rather than earth).
In Heroes 6, after defeating the Thunderbird, it lost some of its power and became smaller. A phoenix is a similar creature and can be of any strength and size.
P.S. I'm reading this thread and I don't quite understand why it was necessary to transfer almost all the units from Heroes 7 here. Wouldn't it be easier to just play Heroes 7 if you're more interested in the canonical plot than in gameplay issues?