Is "This Is What It Means to Say Phoenix, Arizona" an allegory?
I view this story as an allegory with Thomas representing tradition and Victor representing the young Native American man who is angry and feels betrayed by tradition.
I think you are right in arguing that this story definitely has elements of an allegory, though let us remember that an allegory is a story in which every action and character stands for both itself and something else more abstract. Therefore perhaps it is more accurate to point towards the symbolism in this story rather than think of it as an allegory. You are definitely right to think that Victor symbolically represents disillusionment and Thomas represents cultural purity and tradition, and it is clear that there is significant symbolism in the title of the story as well. Let us remember that the phoenix is also a mythological bird that rises from its own ashes and is reborn, so it has become a well-recognised symbol of regeneration.
As the story progresses, this symbolism becomes particularly important as Victor and Thomas reclaim the ashes of Victor's father and the ashes of what has been lost, both in terms of Victor's own life and in a much more figurative sense. The story charts the progression and development of Victor towards being ready to embrace his cultural identity that he has rejected, as is symbolised by the name of Thomas Builds-the-Fire, who has built the fire underneath Victor to enable his regeneration. The flashbacks enable us to understand the series of decisions that Victor has made in his life. The most important of these was his decision to abandon Thomas when they were both young. Victor is able to right this wrong and reclaim the part of himself that he symbolically abandoned along with Thomas through the course of this story.
Thus, while it might not be entirely accurate to think of this story as an allegory in its purest sense, the story owes so much of its power and force to the symbolism that it is based around, particularly in terms of the development and progression that we see in Victor as a character.