Often a personal lesson can help drive home what they need to improve, especially if they're in a large class that focuses more on the kids that DO "get it."
Are they dyslexic, SpEd, or other 504? Do they have computation issues, memory issues, or anything else? Short version: is there a legit reason why their fingers are not "clicking" that moving to a three-button instrument might solve? I'm not saying any of the above CANNOT play flute - but you HAVE TO work harder as a teacher and a player if there are developmental holdups, and the BD should be aware of them if they exist. That's why they call it "differentiation" since they need different instruction.
Check to see where the kid IS, why they're there, and what they need. If you don't feel that you can remediate that kid up to a reasonable level of achievement, then consider switching them - but if the parents have already invested in a flute (on your advice!), then it's incumbent upon you as an educator to TEACH them that instrument.