Did you disconnect the KitProg from the Kit-059?
YES, I just use the kitporg to program the Porcessor Module(CY8C5868AXI-LP035)
Could you open the programmer to check whether the Kitprog can program?
Just a few notes about using Kitprog...
Kitprog SWD wire connections should be as short as possible. 5cm length works well. Greaterthan 10cm causes signal integrity issues.
Also, make sure Kitprog green LED is not flashing slowly. If it is, Kitprog is in bootloader mode. A rapidly flashing green LED indicates it's trying to communicate with target device. You want to see a rapidly flashing green LED.
As Lingling mentioned, try Programmer 3.28. It provides better detail of SWD faults. This will help debug what's going on.
I'm not familiar with the 5LP module, but, is it plugged into another pcb? Kitprog/USB might not have enough +5V current to power up all the circuitry. Try only connecting Kitprog to the 5LP module while separated from other circuitry.
Lastly, can the 5LP module be powered from SWD port? Maybe there's a diode in the path preventing this. Or, maybe there's an option jumper on the module to support SWD powering.
finally I bought a miniprog3 and can program the board successfully.