There isn't a Linux binary; otherwise, you'd find it in the RME download section...
I wouldn't try flashing it via emulation—the emulator might not have the necessary direct access to the hardware.
At best, nothing happens. In a bad case of luck, you get a bad flash result; the worst case would be having to send the device in for service, and this will surely cost around $$$. I wouldn't even try it, and strongly recommend not risking anything.
Firmware updates for this platform aren't released that often anymore, so I'd recommend going to a friend with a Windows PC and flashing it there. That way, you'll definitely be on the safe side.
If you look into the readme file of the last version of FUT, then you will see, that the latest update is from
03/01/2024: Update UFX+ (E) and UFX II (E): Gain of Mic 9 and 10 was coupled with Mic 11 and 12 from +64 dB on. ADI-2 DAC/Pro and 2/4 Pro SE: Extended support for ADI-2 Remote. ADI-2 Pro and 2/4 Pro SE: In Quad Speed, the one possible stereo PEQ is dynamically assigned to the active channel. In Dig Thru mode, ADAT is looped through. ADI-2 DAC AKM: In DSD Direct mode, the volume encoder no longer changes the PCM volume in the background.
BR Ramses - HDSPe MADI FX, M-1620 Pro D, 12Mic, UFX III, ADI-2 Pro FS R BE, Nuendo 15, Win10 IoT Ent