Hyzer flips sometimes add a little extra distance because it's easier to throw higher on a hyzer angle than it is flat. So you throw a high hyzer straight out ahead of you, but instead of going right to left like a hyzer should it flattens out to account for the high speed turn that's kicked in. Throwing it on a hyzer angle means that you can get the disc 25-30 feet in the air nose down, maintaining the disc's speed and giving it more time to turn and flex out because of the added height.
Hyzer flips are also good in the woods, as others have said, because they are so straight with minimal fade. You've got to be very confident in the shot though to use it in the woods--practice with a lot of open sky first.
I think a hyzer flip is a difficult shot to learn. In the beginning, you learn to throw consistently straight plane, anhyzer, and hyzer. Then you can learn to work the discs a bit more to throw turnovers, flex shots, and hyzer flips which are all touchy shots and force you to learn your discs in conjunction with body angles, arm speed, etc. The only way to learn is practice: take a flippy disc (I use a Leopard, Sidewinder, or Comet, all seasoned in) and throw it straight ahead of you on a hyzer angle. It's possible to throw hyzers with these discs too by throwing the disc on a sweeping right to left line but that's not what you want. Throw it in front of you, on a hyzer angle and it will flip and go flat or turn. If it doesn't and hyzers out, you picked the wrong disc or just didn't throw hard enough. If you threw a stable disc that has no turn on this same shot, you would get a hyzer that goes way left of your target, with with the counterbalance of an understable discs tendency to go right, it will equalize and go straight.
Another way to see a hyzer flip is to throw a lid, like an Ultrastar, on a straight ahead hyzer with some snap. They will flip and ride on a sweet line. I don't play ultimate, so I'm no authority, but I can't throw a lid 250' without hyzer flipping it. Also, playing catch with someone who's a football field away may be the most fun way of working on your form.