This is because it is technically a Fighting type move that just happens to do some Flying type damage. It is much like Freeze Dry s simply and Ice type move that is super-effective on Water types. At its core Flying Press is still a Fighting type move, so it will change Kecleon's type to Fighting. Ironically if you use it again on Kecleon, it will still be super-effective because Flying is super-effective on Fighting.
Source: I just used logic, so I haven't tested it or anything (is Kecleon even in X and Y?)