Hi Arun,
What you said somewhat surprises me. It should work. I sometimes use twilight sky for flats, sometimes use an LED panel. On the LED, I just try to keep exposures longer than 1/10 sec, to avoid flickering, and average about 30 of them. For the 30ish exposures, I rotate the LED panel to average out uneven illumination. I also point the camera to different parts of the sky for twilight flat, also to average out potential sky gradient. On my E180ED, I had used Canon 5D2 and Nikon D800/D810A. With this method, I never had problems. The mirror box vignetting is super obvious in the raw file, but it gets flattened out very nicely, pretty much all the time.
BTW, I always take darks (for light, not for flats) and biases, and I use the same ISO throughout.
Cheers,
Wei-Hao