Tightly is generally not the right answer with instruments: it's the fastest way to RSI issues.

I'd have to actually dig out my flute, but I seem to remember the method being to rest it on the thumb knuckle of the left hand, with the right hand supporting most of the weight (as it usually does) on that thumb. It's a sort of rolling motion when you move from having the left thumb down to not, onto the edge of the knuckle.