The flyback transformer is a high frequency transformer that produces the HV for the CRT anode as well as several other voltages. If a replacement part is available then changing it is fairly straightforward but you do have to be careful poking around in monitors. I've repaired CRT monitors for decades and could fix it if you happen to be local to me (Seattle area) but shipping both ways would be cost prohibitive. Whatever the case don't throw it out, CRTs are not manufactured anymore and the last tube rebuilder shut down a couple years ago. What's out there now is what we have and when they're gone they're gone.