What should I consider when buying a saddle?
Comfort
Width/size/fit
Price
Weight
Perineal cutout/groove (if that works for you)
Low friction
Angle your pelvis will be at while riding


That last one is what I suspect Fizik is talking about with the flexibility.  

Assuming you're on a road bike and want to go as fast as possible, being bent forward more will help make you more aerodynamic. As long as getting more aerodynamic doesn't interfere with oxygen intake or leg motion that means going faster.

The part of your pelvis you sit on a saddle is a sort of triangular shape with the point forward, so as you rotate your pelvis forwards a narrower part of that triangle is what you're sitting on. So you need a narrower saddle (and maybe some other shape changes) if you're in a more bent-forward position.

Also take into account that saddle fit is not an exact science, despite the measuring gimmicks many shops have. You'll probably just have to try a few saddles out.