I’ve know that there’s a gizmo key in more expensive flutes ,but I don’t know what it does. How does it help you and is it really useful? 
taytay, this forum is primarily for wooden simple-system flutes, not for Boehm flutes as you are asking about. There are other forums that might serve you better.
The gizmo key is only found on keys with a low-b foot. The gizmo key is a little nubbin or lever, depending on the maker, on the roller for the low-b key which makes it easier to close only the low-b key rather than c-sharp, c and low b. Holding down the b-key is supposed to facilitate playing high c’s and up clearly and in tune.
I use the gizmo on my Boehm flute quite often now that I have a lever-type rather than a nubbin. Some people find them a hinderence when playing low. I know James Galway doesn’t like them.
Ah, cool, I’ve learned something new today.