Leakage current of capacitor
It sounds like you know the current (800uA when 8kV is applied).
It's possible (with a great deal of care) to simply put a milliammeter in series with the capacitor. You should put it in series with the grounded side of the supply so that the meter leads are at approximately ground potential and make sure that connection is reliable. While 800uA is probably not enough to cause injury, it would not be nice. Contact with your supply (the ungrounded side) could result in much higher (possibly fatal) current.
Note that at 8kV you may be getting corona discharge (especially if you have pointy bits facing a strong electric field gradient). This behaves similarly to leakage through the dielectric at a fixed voltage, but will disappear at a somewhat lower voltage (say 1kV).
Edit:



simulate this circuit &ndash; Schematic created using CircuitLab
The 10W resistor is physically large and intended to not break over if the capacitor shorts. If your supply is capable of a lot of current, more precautions may be necessary so this is just a preliminary though. Safety is paramount, so get this checked out by someone local and competent before flipping the power on.