To dump (or flash) firmware of a microcontroller, you have to use an external debugger. I have used a STK3600, that can be configured to be an external debugger.
You can use software like JLink or OpenOCD to flash the target.
The steps below will work for Series-1 microcontrollers (ICC-A and ICC-A-1). The newer microcontrollers are Series-2, for which support is limited or more expensive to get started.
If you use J-Link, you can use the command below to connect to the ICC-1 or ICC-A-1 module:
JLink -If SWD -Speed 5000 -Device EFR32MG1PXXXF256
To dump the flash contents, use the command below (0x40000 is 256 KiB):
savebin output.bin 0x0 0x40000
To load a flash from file, use the following command:
loadbin output.bin 0x0
verifybin output.bin 0x0
I have confirmed that you can dump the flash, erase the device and load it again, and the modules will still work.