Update -
It’s not - he’s Dumbledore’s nephew.
In Fantastic Beasts: Secrets of Dumbledore, it’s revealed that Credence is actually Dumbledore’s nephew, and Aberforth’s son. Aberforth had a fling the same summer that Dumbledore met Grindelwald, the woman was sent away but had a child - Credence.
It can’t be - Dumbledore’s parents died too long before his birth.
Dumbledore’s parents both died before they could possibly have another child Credence’s age. When he was hunting Hallows with Grindelwald, the reason that Dumbledore was so interested in the Resurrection Stone was to bring his parents back so he’d be free of responsibility to Ariana.
“And at the heart of our schemes, the Deathly Hallows! How they fascinated him, how they fascinated both of us! The unbeatable wand, the weapon that would lead us to power! The Resurrection Stone – to him, though I pretended not to know it, it meant an army of Inferi! To me, I confess, it meant the return of my parents, and the lifting of all responsibility from my shoulders.”
- Harry Potter and the Deathly Hallows, Chapter 35 (The Deathly Hallows)
Since he wanted to bring both of his parents back, his father would have already died in Azkaban by then - the Resurrection Stone is said to bring people back from the dead, not free them from Azkaban. If he thought that the Stone would bring back his father, his father would have to be dead. His mother was also dead, because her death was why Albus became responsible for Ariana. She died when Albus was around eighteen - he’d recently graduated and was close to leaving for his traditional post-graduation tour of the world before she’d died.
“When Albus and I left Hogwarts, we intended to take the then traditional tour of the world together, visiting and observing foreign wizards, before pursuing our separate careers. However, tragedy intervened. On the very eve of our trip, Albus’s mother, Kendra, died, leaving Albus the head, and sole breadwinner, of the family. I postponed my departure long enough to pay my respects at Kendra’s funeral, then left for what was now to be a solitary journey. With a younger brother and sister to care for, and little gold left to them, there could no longer be any question of Albus accompanying me.”
- Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
He was around seventeen when he met Grindelwald, which would be when he sought the Hallows.
“And what ideas they were. Profoundly shocking though Albus Dumbledore’s fans will find it, here are the thoughts of their seventeen-year-old hero, as relayed to his new best friend (a copy of the original letter may be seen on page 463):”
- Harry Potter and the Deathly Hallows, Chapter 18 (The Life and Lies of Albus Dumbledore)
He’d only spent two months planning with Grindelwald, so he wouldn’t have aged much in that time.
“Invincible masters of death, Grindelwald and Dumbledore! Two months of insanity, of cruel dreams, and neglect of the only two members of my family left to me.”
- Harry Potter and the Deathly Hallows, Chapter 18 (The Life and Lies of Albus Dumbledore)
Dumbledore’s birth year was stated to be 1881 on his Wizard of the Month card, which was written by J.K. Rowling and featured as part of her old website.
Dumbledore’s parents would have to have both been dead by 1899, since he couldn’t have been more than eighteen when he was hoping to bring them both back with the Resurrection Stone. This would mean neither of them could possibly be Credence’s parent. Credence was able to be confused with another baby, Corvus Lestrange, who was born in 1901, so he’d likely have to have been born around then as well. Dumbledore’s parents would already have been dead then, for sufficiently long that his father couldn’t have conceived Credence before dying, even with another woman, if he somehow escaped from Azkaban, and his mother couldn’t have died while having Credence. They would have been dead around two years before Credence was born, so they wouldn’t have been able to have him even right before dying.
SCENE 103 INT. LESTRANGE MANOR, BEDROOM—1901—DAY
We reenter the story to find LESTRANGE SR. with a new, blond wife.
KAMA (V.O.)
He remarried not three months after her death. He loved her no more than he had loved you . . . But then . . .
IRMA takes the BABY BOY who has just been born, and passes him to LESTRANGE SR., who is delighted.
KAMA (V.O.)
. . . his son, Corvus, was born at last. And that man who had never known love was filled with it . . .
- Fantastic Beasts: The Crimes of Grindelwald (The Original Screenplay)
In Fantastic Beasts: The Crimes of Grindelwald, it seems that Dumbledore’s birth year is fairly consistent with this - he’s forty-five in 1927. Simply subtracting his age from the year gives 1882, but if his birthday is still yet to come at that time, it may still be 1881. Presuming that the events occurred at the same time in Dumbledore’s lifetime in the movies as in the books, his parents would still be dead too long to have Credence in the movies’ timeline.
SCENE 27 EXT. DOME OF ST. PAUL’S—EVENING
Apparating beside a dandyesque forty-five-year-old wizard with graying auburn hair and beard. NEWT hands back his glove.
NEWT
Dumbledore.
- Fantastic Beasts: The Crimes of Grindelwald (The Original Screenplay)
So no, it isn’t possible by previously established canon that Credence could be either Dumbledore’s full brother or half brother, since his parents both had died before Credence was born. However, as Valorum says in the comments, JKR has already broken canon for the movies, so this doesn’t mean that it’s not going to be shown as true in the next movies - she may simply ignore the dates that were established for Dumbledore’s family, like she did when she de-aged him down from 150.
Maybe it’s not, we don’t know if what Grindelwald said is true yet.
Credence being Dumbledore’s brother isn’t truly confirmed yet - Grindelwald says he is, but it’s also clear that Grindelwald is willing to lie to people and manipulate them to get them to join him. He caters his approach to each person, like telling Queenie they’ll build a world where she can marry Jacob. He knows Credence is desperate for family, and he’s certainly playing the long con.
GRINDELWALD
So . . . Credence Barebone. Nearly destroyed by the woman who raised him. Yet now he seeks the mother who bore him. He’s desperate for family. He’s desperate for love. He’s the key to our victory.
KRALL
Well, we know where the boy is, don’t we? Why don’t we grab him and leave!
GRINDELWALD
(to KRALL)
He must come to me freely—and he will.
Grindelwald specifically wants Credence to find out his heritage from him (killing off Irma to ensure it), and he lays out a path for it to happen, so Credence will be led right to him to learn his heritage.
GRINDELWALD returns his gaze to the vision of CREDENCE suspended in the center of the drawing room.
GRINDELWALD
The path has been laid, and he is following it. The trail that will lead him to me, and the strange and glorious truth of who he is.
- Fantastic Beasts: The Crimes of Grindelwald (The Original Screenplay)
Grindelwald specifically wants Credence to kill Dumbledore, so there’s a clear reason he’d want to make Credence to hate Dumbledore. Portraying him as the brother who abandoned Credence would be a good way to turn him towards Grindelwald and against Dumbledore.
GRINDELWALD
Who represents the greatest threat to our cause?
KRALL
Albus Dumbledore.
GRINDELWALD
If I asked you now to go to the school where he is hiding and kill him for me, would you do it for me, Krall?
(smiles)
Credence is the only entity alive . . . who can kill him.
- Fantastic Beasts: The Crimes of Grindelwald (The Original Screenplay)
There’s no reason to presume that Grindelwald is telling the truth yet without further confirmation. Even the phoenix may not be what it seems - Grindelwald is extremely talented in Transfiguration.
5. Why did ‘revelio’ undo the effects of Polyjuice Potion?
It didn’t. Grindelwald’s Transfiguration surpasses that of most wizards, so he used a spell, not a potion, to take on the appearance of Percival Graves.
- Welcome to my new website! (J.K. Rowling’s website)
In addition, Credence only was seen with the chick after he encountered at least one person who was confirmed to be working for Grindelwald - Grimmson, who killed Irma for Grindelwald to further his plan to lure and recruit Credence. He, or another one of Grindelwald’s followers, could have put the chick on or near him for him to find. It could even be a real phoenix - Grindelwald would have known both his own plan to turn Credence to his side against Dumbledore and the legend about the Dumbledore family’s phoenix connection, so could have arranged to get a phoenix, they’re rare but not impossible to find. There’s no reason to think Grindelwald is telling the truth yet. If he really is telling the truth, it’s likely to be confirmed in later movies, but for now it’s early to think Credence is actually Dumbledore’s long-lost brother - he still might not be.