You have nostrils. Learn to inhale and exhale at the same time. Become the master of your own body. Defy your limitations. You're playing the flute, goddammit! Give it the respect it deserves, and transcend beyond your mortal limitations and grasp the freedom of the ethereal.
Lol I tried this for two breaths and already got a head rush. I'm not even trying to play an actual flute, just sustain pressure from my mouth while I inhale and then switch back to blowing from my lungs.
I wonder if master flutists get a kind of natural high any time they play at a high level that uses this technique and that's why they stuck with the flute long enough to master it.
Or hell, if dopamine for non-ADHD people gives good feelings from normal stuff, is that why anyone sticks with things long enough to master them? Just flute masters might get that extra head rush on top of it.
You can legitimately do this with brass instruments, I don't know about woodwinds. You puff up your cheeks and use them as a source of air kind of like the bag on a bagpipes ('bagpipes' is singular I decided) while you sniff a breath through your nose. You can sustain a note until you get bored. Don't know if you can puff out your cheeks with the mouth shape you need to play a flute.