I had this issue about two weeks after replacing a broken screen myself. I tried all the software solutions, but none worked for me (not allowing the screen to go dim did, but I didn't like that solution). The screen would also not turn on when pressing the power button. The issue with mine was the digitizer was not fully secured to the phone. If I pressed the top of the screen down (around the speaker and/or light sensor areas), the flickering would stop and the screen would turn on fine. I didn't use tape to replace my screen, but just let the residual glue hold it, which apparently was not enough. Also, I noticed the former screen popped right off without using any heat. It seems the hot summers and normal use wore the factory glue down to almost nothing. If the software fixes don't work for you, consider worn out glue and a digitizer separating from the phone as the issue.
Best of luck to you all!