Have you looked at the website
www.fearofflying.com? Many years ago several airlines had fear of flying classes. I took the one offered by American Airlines that IIRC was called AAirBorn. It gave you tools to handle your anxiety when flying. I used some of the tools, but I found the thing that helped me the most was reading a book to take my mind off the fact I was flying in an airplane. In your niece's case maybe doing puzzles will help take her mind off the fact she is flying.