A good thing to do is practice deep breathing when you are NOT playing the flute. Do it in the morning when you're lying in bed, or right before bed at night (depending on whether you find the extra oxygen invigorating or relaxing <g>
. Put your hand on your belly. Exhale fully, and then take a deep slow breath. Your hand should rise as your diaphragm moves down. Fill your lungs from the belly up. Then slowly exhale. Do this a couple of times per day. Once you're used to the feeling, you can do it any time--practice it both standing and sitting, as you won't normally play your fluting lying down.
BTW, I actually learned this when I was pregnant, not in flute lessons.
But, it really is the correct way to breathe, and practicing it will help a lot with the lightheadedness, as long as it's simply related to your body getting used to the extra oxygen intake and/or the need to fully empty your lungs to complete a musical phrase.
<Added>I have no idea where that winky face came from--the software obvious ate my closing parenthesis. However, I'm not sure I like what it implies about the previous sentence, so I figured I'd note that it isn't meant to be there. :)