Rohan,
Flash Magic for programming the NHS3100 and LPC-Link2/CMSIS for program debug have a tendency to retain possession of the PC connection and not let it go for each other. I found that I had to take one completely down, kill its program, and remove its connection before I could bring the other up the other. It helps to open up a printers and devices menu on the PC and watch for the device connection to appear/disappear before continuing. I have noticed that LPCXpresso V8.2.2_650 and Flash Magic V11.20 are somewhat better. At least you don't have to kill the program(s) now, but you do have to wait for the LPC icon to disappear from 'devices and printers' before plugging USB back in to connect again for the opposite program. Good luck!
One could wish that NXP would integrate Flash Magic or include some of its useful features with their debug/CMSIS programmer, like reading or erasing sections of Flash, verifying checksums, etc. But I guess MCUX has taken over, leaving LPCX without development resources.
Steve