I just got my X100F for almost a week already and I noticed that during on autofocus (single point) I noticed that the screen is flickering on half press even when I am trying to focus the same subject over and over. Though it does not affect any of the output images produced by the camera but I just want to understand the behavior of the camera because as far as I remember it is not happening on my X70 and X100T.
Recent Fujifilm cameras use a hybrid Phase-Detect and Contrast-Detect AF system. What you are seeing is the Contrast-Detect loop which causes the lens to move back and forth in order to confirm the distance of highest contrast.
If there is a stronger flickering indoors it could be due to the cycling of lights, mostly fluorescent that go on and off at 60 or 50Hz. With a very fast readout, this is much more noticeable than on earlier Fujifilm cameras since each read of the sensor takes a shorter time and catches the flickering.