Just so you guys know, the Pheonix at the funeral was NOT Fawkes, the previous chapter precludes that possibility. It COULDN'T have been Fawkes. I'll explain why in just a minute.
Anyways, I also came up with the Pheonix idea soon after finishing HBP, just like the person who posted this thread. Here is my take on it. First, some key things that should be noted:
1. Dumbledore has a pet Pheonix, Fawkes.
2. Dumbledore's Patronus is a Pheonix.
3. Dumbledore is VERY old, yet up until near his end, he remained spry, youthful, and energetic. He was wise, but certainly not a tired old man. BUT, at the end of OotP and several times througout HBP, it was noted that he was starting to grow tired at last.
As I see it, Dumbledore is the very embodiment of a Pheonix. Now, if anybody has powerful secret abilities, it's Dumbledore. I can see no reason why he WOULDN'T be a Pheonix animagus.
So, with this idea, it could be possible that Dumbledore, who was finally growing tired near the end, was reborn from his tomb in his Pheonix form. As you know, Pheonix's do grow old and tired, and then die, but afterwards they are reborn. Fawkes did that in Chamber of Secrets. When Harry first saw Fawkes he looked very ugly, because he was on his last limbs. Then he burst into flames and was reborn, to eventually reach adulthood again. I feel that at the end, Dumbledore was getting to that same point of "final" exhaustion. When he died, the flames rose up as he was reborn as a Pheonix, and flew away.
But, for you skeptics who say it wasn't Dumbledore, it was Fawkes, just look back at the end of chapter 29, "The Pheonix Lament", from Half-Blood Prince.
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"Dunno," said Harry, lying back on his bed fully clothed and staring blankly upwards. He felt no curiousity at all about R.A.B. He doubted that he would ever feel curious again. As he lay there, he became suddenly aware that the grounds were silent. Fawkes had stopped singing.
And he knew, without knowing how he knew it, that the phoenix had gone, had left Hogwarts for good, just as Dumbledore had left the school, had left the world...had left Harry.
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That line still makes me sad.

But the point is, that little excerpt clearly states that Fawkes had left Hogwarts for good, and he was not coming back. Dumbledore's funeral wasn't until the following chapter, so it couldn't possibly have been Fawkes that encased Dumbledore's body in the tomb, could it? No, I believe that it was Dumbledore, giving his former life a proper goodbye and a proper burial before he left, finally free from the shackles of old age.
Whether he will remain a Pheonix forever or he can return to wizard form, I'm not sure (probably the former), but I'm pretty sure it was Dumbledore that ignited the table and created the tomb. I'm pretty sure he's still in the world of the living in some form, not just in the afterlife.
An alternative to the animagus theory is a theory using Harry's wand. It contains a Pheonix feather. Perhaps this could be used to revive or communicate with Dumbledore in some way...just as long as he doesn't "pull a Gandalf", this might actually be possible.