The position of the right hand during flute playing is one of the things I find myself correcting most often in my beginning students. This is partly because it's hard to be aware of what the hands and wrists are doing when you're first learning an instrument, and also because improper hand position can lead to overuse injuries down the road. My goal is to help my students avoid these injuries so they can play their instruments pain-free and enjoy as many years of music-making as they want.
Take a look at the pictures below: the images on the right and left show the different ways the wrist can be forced into an unnatural, damaging position, while the center image shows what a healthy, neutral wrist and hand look like.
This isn't exclusive to flute players, by the way; everyone should be aware of this. Whether you play the flute, another instrument, or none at all, take some time during your day to check in with your wrists. They'll thank you for it!