I have the problem flashing the MSP430FR5739 device with Olimex MSP430-JTAG-TINY-V2 using CCS v6.1.3. The error message is:
MSP430: Trouble Writing Memory Block at 0xc200 on Page 0 of Length 0x56: Could not write device memory
MSP430: File Loader: Verification failed: Target failed to write 0x0C200
MSP430: GEL: File: C:\ws6.1.1\rs485-rs232\Debug\rs485-rs232.out: Load failed.
It is flashed OK with FET430-UIF JTAG.
The Olimex MSP Programmer software does not provide any MSP430FRxxxx as option.
MSP430-JTAG-TINY-V2 doesn't work properly with CCS v6.1.3 or newer since it requires tools that implement MSP430.dll v3 protocol. The firmware of MSP430-JTAG-TINY-V2 implements MSP430.dll v2 firmware. This is mentioned in bold on the product page of MSP430-JTAG-TINY-V2.
I would recommend using an older version of CCS.
In fact, I'm using CCS v6.1 with this JTAG for all devices successfully, and only problem I have is with MSP430FR5739.
It seems that it doesn't work properly with the latest firmware here too. But it seems to work fine with older firmware. Try using this firmware: https://www.olimex.com/Products/MSP430/JTAG/_resources/OLIMEX-MSP430-DLL-drivers-1.042.zip
Close CCS, navigate to C:\ti\ccsv6\ccs_base\DebugServer\drivers and backup all dlls (in a separate folder) then copy the dll files from the archive that was linked above.
When starting debug session you would be asked to update the firmware of the unit, select to update it. I've uploaded picture below. I used Windows 10 x64 and CCS 6.1.2