Flat shooting is not more accurate. It is just easier to aim.
All bullets travel in an arc. If the bullet is fast enough, the useful range of the bullet comprises more of the first part of that arc, before the bullet starts to sink quickly from the observer's point of view.
So the gun that has a higher velocity for longer will generally be flatter shooting. Keep in mind that a bullet that starts faster, but has higher drag, might slow down below the comparable round. So it isn't just muzzle velocity that counts, but downrange velocity.
That all sounds technical, but "flat shooting" is not a technical term. It is just a name for a fast cartridge that doesn't need great elevation corrections as you extend range. 9mm (1200 fps) is flat shooting compared to .45 (850).