Except for it being a boy who teaches the children to fly (rather than a girl in the original question), this fits very well with The Summer Birds, a short novel by Penelope Farmer. First published in 1962 it is definitely possible for it to be in a school library in the 1970s.
The central characters are the sisters Charlotte and Emma Makepeace, who live with their grandfather in a country house called Aviary Hall in the south of England. From the wikipedia summary:
On the way to their small English village school, they meet and
befriend a mysterious boy who tells them that he is able to teach them
to fly. Over the following days and weeks, the boy teaches Charlotte
to fly, and then the other children at the school learn this ability.
Their schoolteacher, Miss Hallibutt, discovers them flying, and asks the boy to teach her too:
"I suppose ... I suppose ... I cannot learn to fly too?"
The boy said apologetically: "No, I can only teach children. You—you
are too old."
"Yes, I feared that," said Miss Hallibutt sadly. "You are lucky
children. I always wanted to fly at your age— once—once I nearly did.
And I suppose as you're here," she said to the boy, "I suppose you had
better come to school. And mind you behave.
Rather than having a "Phoenix imagery", I would say the boy has a more of a Peter Pan air - his aim was to get the children to fly to his homeland where they would never grow up.
The book is available to borrow free of charge from the Internet Library.