I would compare FLrig to Hamlib since they are both programs written to control various radios. Hamlib does radio control and doesn't try to do more. FLrig does radio control but also has an on-screen display capable of radio control. Hamlib requires the main software (such as WSJT-x) to set the radio frequency and all other functions. FLrig accepts radio commands from software like WSJT-x, but can also control the radio and adjust its features with the FLrig "radio console" software.
I'd say leave Hamlib in control if at all possible. Craig has integrated Hamlib into Digipi and it usually works great. The main reason I ever looked at FLrig was to use it for the radio console display and control feature in case of SSB voice operation. My theory is that FLrig could be a replacement for the proprietary radio console software in the MFJ Rigpi. OTOH, I'd have to decide if using FLrig to avoid the warts in the Rigpi software is worth the effort. For the Digipi software, I probably wouldn't bother with FLrig. As long as FLdigi can use Hamlib, you probably don't need FLrig.
But for your purposes of testing the Network105 software, if you need to use FLrig, be sure to save your current working version of Digipi and make a new image on a new SD card before you start changing things. When I was playing around with FLrig and WSJT-x, I found it a bit confusing to get working. There are a lot more web sites and directions for using Hamlib with all the usual digital software and fewer sites explaining FLrig. I ended up going down the rabbit hole several times before I got it working.
Good luck!
73, Doug Reed, N0NAS.