I have a 2002 XJR with two issues fuel related. First, it is difficult to start hot, starts perfect when cold. Second, it will not accelerate, when you step on the accelerator it bogs down.

I have replaced the fuel filter.

I ran a fuel pressure test and when you first connect there is only 2 psi, when you switch the ignition on to position 2 there is no change in pressure. After starting the motor it very slowly (15 to 20) seconds increases up to 32 psi, I increased the idle speed to around 2000 RPM and there was no change. I removed the fuel pressure regulator line and capped it and again there was no change, it remained at around 32 psi. After shutting off the motor the fuel pressure immediately dropped to around the 2 psi mark.

Any ideas if it is regulator or fuel pumps?

 

Pinch off the vacuum line at the regulator first and then remove it. Your fuel pressure gauge should go to about 45 if working properly. From what you're saying about starts fine cold, but not hot sounds just like a fuel pump. If you ever go into the fuel pumps, replace them both.

You said the fuel pressure gauge slowly goes up. Taking a fuel pressure reading can be a little bit tricky. I've had to remove the schrader valve from the fuel rail and the opposing valve in my fuel pressure gauge hose. If you can seal it up, I'd remove both valves and see if that improves your readings.

 

I did remove the vacuum line from the regulator and there was no change in pressure. I also did attach a vacuum pump to the fuel pressure regulator and applied around 5 psi and it held for a couple of seconds and then very slowly went to 0 which from what I can find is normal.

 

Not trying to be negative, but it sounds like a grenading primary fuel pump. The fuel isn't keeping the pump cool enough and when it heats up, she binds up. If that's the case, replace both.
I'd do some more testing, but your easy start cold and hard start when hot is my indicator.