I have an FT-991 with just a USB cable to a Windows 7 laptop, and use CAT with FLDIGI and many more programs.
As you mention OmniRig, I suspect with FLDIGI you've run into the problem that 2 different programs (FLDIGI and OmniRig) can not share a COM port.
However, with a Splitter (VSPE free 32-bit) it works fine, at least for me all the time, even if it shouldn't.
As a precaution I use specific startup orders, e.g one or more of FLDIGI, N3FJP AClog, HDSDR/CW Skimmer or WSJT-X/JS8Call, all the latter using OmniRig (which is safe for sharing a COM port). My FLDIGI uses RigCAT and AClog it own scheme, and the rest OmniRig, so there are 3 users of the COM port. The more Win apps that use OmniRig, the better.
You could look at my FT-991 and FLDIGI settings at www.sa7cnd.se
If you use the VSPE Splitter, remember to turn on the rig first so USB/COM activates and then VSPE. Also, stop VSPE on the Stop button (or shut down Windows) before turning your rig off.
Good luck. 73 de Poul SA7CND