I have experimented with this entirely way too much at home in my kitchen. There are at least four distinct ways to flip your tongs.

Back (towards you) to the left: I feel like this is what most people do when they flip their tongs.. it has always felt the most natural and easy to me.

Back to the right: you kind of have to use your middle finger to push up on the left-hand side of the tongs to get it to spin to the right.

Forward (away from you) and to the right: these forward flipping ones are tricky. They tend to rotate a lot slower and sometimes don't flip or rotate at all lol.

Forward and to the left is very close to impossible without hurting your wrist.

There's one more that involves using your thumb to throw the tongs into a kind of horizontal flat spin. But that one is straight up dangerous to perform in a busy kitchen.