<p>For film score studies, I believe University of Southern California would be a very good option. Among the Ivy Leagues, Princeton also has strong composition and theory faculty although there is no major in composition. Northwestern is another option.</p>
<p>To return to the OP’s concerns, we didn’t know it was possible to take composition lessons privately, and my son applied to Juilliard pre-college with hand scribbled manuscripts and absolutely no private lessons, and was accepted with a big scholarship. What he did have under his belt was a ton of music theory, and that is fairly easily obtained, whereas finding a really compatible and excellent composition teacher might be more difficult. As part of music theory courses, your daughter would be assigned composition exercises and I almost feel that is a preferable way to begin. A teacher can have certain prefixed ideas and there is always the risk of squashed creativity.</p>
<p>Also, would like to say here–though it’s been said elsewhere–that performance level on an instrument is really not a huge component for a composition student. So the OP shouldn’t worry about her daughter’s level flute playing–she is obviously competent enough to qualify for any conservatory or college composition major.</p>