I've found a lot of examples of expression "Get in a flap" but in my coursebook the expression is said with "into" instead of "in". Are those prepositions interchangeable or is that an error in the book?
The expressions are interchangeable, and ngrams suggests that both forms are about equally common (in the books that Google has scanned)
In general, saying "He got into the box" and "He got in the box" have the same or very similar meanings. But when used without an explict noun, only "in" is used.
Hitchhiker: I want a ride to London
Driver: Sure. Get in.