How does phantom spd work?

It works exactly the way it says it works.

It's pretty straightforward - when using a skill like Flashing Blade or Windsweep, Phantom Speed will pretend that your unit's Speed is 5/8/10 points higher than it really is, making those skills easier to activate. It doesn't actually increase your Speed stat, though.

If it doesn't appear to be making a difference, make sure that the enemy units don't have skills that are increasing their Speed during combat.

It only works on skills that compare the speed of two units (including stuff like Sylgr, but that's a pretty inefficient choice of seal for her); it will not help you double unless the skill grants a forced double based on a spd check.

It's usually used with sweep skills. I have it on Saizo with watersweep right now