Hello chrisc@rmlgroup.com,
Just to clarify some things here:
The LED is still blinking multiple times, so I am not sure if flashing from S32DS is going to fix that. If it does not, then could anyone provide links to documentation to flash my other binary/ELF files for the builds I did? I've created a project but don't know how to point it to the files.
The Model-Based Design Toolbox for S32K generates the code and then compiles the generated code, resulting a .elf file. From this .elf file it then generates a .mot file and copies this .mot file to the OpenSDA. The OpenSDA takes this file and flashes the controller with over SWD.
If you need to debug or program the generated code, you can import the .elf file in the Debug Configuration or S32DS and once you selected a valid project for your board (I am using the hello_world_s32k144 provided by the SDK) you can press browse and select the desired .elf file. It will flash the file that appears in the c/C++ Application field

Another possibility is to import the whole generated code in the S32DS, ONLY if you need to debug or so, but just for flashing is not necessary.
In any case, for me it is 100% important to have the USB functioning so I can use FreeMaster.
OpenSDA uses for flashing the SWD protocol and dedicated pins connections [2]. The FreeMaster communicates over the Serial and uses the OpenSDA as a USB to Serial converter on pins [1]. OpenSDA can't be used as flashing tool and as USB to serial at the same time, even if there are different pins. But once the program has been flashed, you can use the Serial no matter which method of flashing you have used: copy paste the .mot file or S32DS.

Hope this helps,
Marius