Our diaphragm is an involuntary muscle (we don't control it---thank God, we'd all die if we actually had to initiate and control it's function

), so, really, it's our abdominal muscles we use to control our breathing when playing a wind instrument. Keep your ribcage expanded after your first big breath when beginning to play, and maintain good, "tall" posture (think "ballerina"), but not strained or exaggerated--stay flexible and relaxed. It takes too much time (and energy) to have to re-expand the intercostal muscles, between our ribs, for each breath we take.
Do use your abs to support your airstream, kind of like squeezing toothpaste from a tube, but, otherwise, avoid tension in your body. Don't think of vacuuming in huge quantities of air (that's for later, lol), rather allow your lungs to inflate. This doesn't eliminate inhaling, of course, but imagine the air going into your lungs like water pours into your mouth if you open it in the swimming pool! Think of filling your lungs from the bottom, up. An exercise to try: lie on the floor, relaxed, and place a book on your abdomen, sort of below your ribcage. Take long slow breaths, trying to elevate the book,
not your chest. You can do this in counts, like eight slow counts to inhale and eight or twelve counts to exhale in a controlled manner. Another, to determine
where to breathe: stand up, place your hands on each side--palms on your hipbones, fingers extending across your lower abdomen. Bend at the waist. Breathe deeply, feeling your hands move. Stand up again, with hands still in place. Breathe again, still feeling movement under your hands. When playing your flute, try to breathe all the way down there! Sounds confusing, but after it becomes a bit more habitual, you won't have to think about it.

Good luck!!!

P.S. If you're interested in the physiology of breathing as it relates to wind players, check out books by Arnold Jacobs, former Chicago Symphony tubist. I think
www.Amazon.com has them.