How old is Fawkes the Phoenix?

Question

How old is Dumbledore's phoenix, Fawkes?

Neither the Wikipedia entry on Fawkes nor the Pottermore article mentions his age.

My motivation is mostly curiosity, but also because I believe the age might tell us something interesting about Dumbledore.

If Dumbledore adopted Fawkes when the bird was young, then perhaps Fawkes chose Dumbledore because it was raised by him. Or perhaps it had not lived long enough to know many humans and accepted one of the first humans to care for it.

But if Fawkes is of immense age (centuries or millennia old), then it has encountered hundreds or even thousands of humans over its many years. For Fawkes to choose one particular human, Dumbledore, among all those it met means that Dumbledore was truly someone special to it.

Garrick Ollivander, the wand-maker, uses their tail feathers to make wands. Ollivander prefers to use only three animals for wandmaking: unicorn hairs, dragon heartstrings, and phoenix feathers. One might think phoenixes were somewhat common for their feathers to be used for such a common tool. Yet, to my best knowledge, none of the Harry Potter stories even mentions anybody else owning another phoenix, or even mentions a phoenix besides Fawkes.

Answer 1

Unknown

J.K. Rowling has only once spoken about Fawkes past

Peter Humphreys for BBC Newsround - Who did Fawkes previously belong to and will he play a vital role in the next book?

JK Rowling: I am not going to answer about the role in the next books, which probably gives you a big clue, and he has never been owned by anyone but Dumbledore. You will notice that when Harry goes back in the Pensieve in this book, Fawkes is never there, and ­­ no, I am sorry, not in this book, I take that back. When Harry has previously seen the study with a different headmaster he saw it with Dippet and Fawkes was not there then. Fawkes is Dumbledore's possession, not a Hogwarts possession.
_{(Edinburgh "cub reporter" press conference, ITV, 16 July 2005)}

HP wiki does like to point out that the fact that his feather provided the core for Voldemort's wand would place a bare minimum on his age as being born slightly before 1938.

“Exactly,” said Dumbledore. “Harry’s wand and Voldemort’s wand share cores. Each of them contains a feather from the tail of the same phoenix. This phoenix, in fact,” he added, and he pointed at the scarlet-and-gold bird, perching peacefully on Harry’s knee.

“My wand’s feather came from Fawkes?” Harry said, amazed.

“Yes,” said Dumbledore. “Mr. Ollivander wrote to tell me you had bought the second wand, the moment you left his shop four years ago.”
_{(Harry Potter and the Goblet of FIre - Chapter 36)}

Of course, Fawkes had lived in the wild before Dumbledore domesticated him, and he probably did not provide the wand feathers until some later point. Fantastic Beasts and Where to Find Them tells us that Phoenix's generally live to "an immense age", so we really have no way of knowing how old Fawkes is.

The phoenix lives to an immense age as it can regenerate, bursting into flames when its body begins to fail and rising again from the ashes as a chick.
_{(Fantastic Beasts and Where To FInd Them - Phoenix)}

Answer 2

Not a lot about Fawkes origin in known. A reasonable estimate of his age is provided at link. It is stated that he was born on or prior to 1938, and aged at least 79 years.