I might try using cross-body or Brain Gym activities with the whole class. Eb to F can be an easy fingering for most students, but it’s also one of the few first notes on the flute that has the hands moving in two different ways- the left hand puts a finger down while the right hand lifts two fingers. Contrary motion can be hard for students that don’t have that coordination yet (and, as a woodwind player, it’s something I try to avoid whenever possible). Working on getting both halves of the body to move independently takes time and practice, and the rest of your class might find Brain Gym activities fun, too.
Playing songs by ear might help, too. There are tons of different five or six note songs that she could try, and not focusing on notation might free her up to focus on her fingers.