A common problem for flutists is the note that wheezes or doesn't speak at all. Our lowest and highest notes are usually the ones that challenge us, but others can, too.
Today I had an experience that reminded me of a very important point: the note that doesn't speak isn't always the culprit! The problem may be the note before or after it, or even several notes away!
Consider today's challenge: first octave, middle C. The preceding notes were moving donward: A-G-E flat; then the C began a scale moving upward, C-D-E flat-F-G-A ....
When the E flat was wheezing, and the C not speaking at all. Of course my first thought was to focus on C, which is always a challenge. But upon slowing down and playing the preceding notes, I discovered that my left hand fingers were not covering the holes well, and although the G sounded, it wasn't a good note, and as soon as I fixed the G, I no longer had problems with either the E flat or the C.
So, the next time a note is giving you trouble...take a good look at several ones leading to it and following it. Good luck!