I've had the new rotors and pads (Centric Posiquiet semi-metallic) on the car for about a week, and I'm getting pretty loud squealing from the brakes on medium pressure stops (hard pressure stops are quiet). The shop that installed them (very sharp guys) took a second look at the shims and applied some sort of compound to the pads, but i'm still getting the squealing.

Is this something that should get better over time, or do I need to look into alternate brake pads than the Centric Posiquiets? The squealing is quite annoying and loud.

 

The two year flush is not unique to Jag. Almost all OEMs recommended this or a similar interval. It's actually an overly conservative thing left over from the dark days long ago when brake master cylinder reservoirs were vented directly to the atmosphere.

The Jag fluid is nothing special. It's just regular stuff relabelled. All brake fluid of the same DOT rating is interchangeable, no need to worry about intermixing brands.

 

I have the same pads on stock (machined) rotors.
They don't squeak, instead they "graunch" just as I come to a stop.
Nothing I have tried has reduced this graunch, so I'm living with it until it's time to replace the rotors and pads together.
As for squeak, I've had that problem on earlier cars and I fixed it every time using CRC de-squeak, see here: CRC 05080 de Squeak Brake Conditioning Treatment 11 25 oz Each | eBay
Spray it on both sides of the rotors, then burnish it on by getting the brakes good and hot - repeated hard braking from highish speed. Keep doing it until you can see and smell grey smoke. In effect an "Italian tune up" of the brakes! Most times I've had to repeat the exercise a week later, and then no more squeak ever.

 

I have the same setup with the posiquiet ceramics (vs semi metallic) and I've had no noise issues. Try the anti squeal paste/spray and hopefully that fixes it. You have solid or drilled rotors? Drilled / slotted (which I have too) seem to be more susceptible to this, but it's definitely possible to have it silent!