The Body as Experiment: Jeff Brown, Flat Stanley, illustrated by Tomi Ungerer (New York, Evanston, London: Harper & Row, 1964).
I’ve included this book as sf because the facilitation device is mechanical, not mystical.
Quite a famous book I believe: Stanley is squashed by a picture board and comes out flat. He can slide under doors, and through gratings. His younger brother gets jealous and Stanley allows Arthur to fly him as a kite. There is an exciting period in which he is a hero after he helps catch robbers (he poses as a picture of a Shepherdess in a museum), but then the public turn against him and he is mocked. His formerly jealous younger brother uses a bicycle pump to blow him up again and return the family to normal.
I like the way the child is encouraged to play with possibilities and to think about what their own body can do. Lurking behind the story is “what can I do with a human body?”
There are a number of books in the series. The much later Invisible Stanley (1996) follows a similar trajectory to Flat Stanley, but Stanley In Space (1990) is a straightforward meet the aliens story in which the threatening aliens turn out to be Lilliputians who have run out of food. Stanley rescues them and brings them to Earth for a year while their lands recover.