“He seemed a charming boy to me,” babbles Bathilda, “whatever he became later. Naturally I introduced him to poor Albus, who was missing the company of lads his own age. The boys took to each other at once.” They certainly did. Bathilda shows me a letter, kept by her, that Albus Dumbledore sent Gellert Grindelwald in the dead of night. “Yes, even after they’d spent all day in discussion—both such brilliant young boys, they got on like a cauldron on fire—I’d sometimes hear an owl tapping at Gellert’s bedroom window, delivering a letter from Albus! An idea would have struck him, and then he had to let Gellert know immediately!”
-- from The Life and Lies of Albus Dumbledore by Rita Skeeter
Wizaring version of “they got on like a house on fire,” i.e. very, very well.