I have found that a single flip is best.
The meat will actually tell you when it is time to flip. Presuming you start with a clean, well seasoned grill/grate at a nice high temperature the meat will stick until it is ready to be flipped. Nudging it's side gently to test it's cling will let you know; if it slides, it is ready to be flipped.
Once it is on its second side I find it is best to leave it alone until it passes the finger-thumb test. Touch your pointer finger loosely to the tip of your thumb (on the same hand) and then poke at the fleshy area at the base of your thumb. The denseness, or 'give' of your muscle there is the same as a steak should feel when cooked to rare. Your middle (bird) finger touched to your thumb will give you the texture of a medium rare. Your ring finger is medium, and your pinkie will give you well-done.
If you are really keen on cross-hatch grate marks I suppose you could flip two more times. Just remember that the meat will take heat out of the grate during cooking (as well as warming to a less contrasty temperature) so it'll take a bit more to get the second set of marks. So four flips max, for the pretty. If you flip more than that, that's just silly. Stop that.