I'm an amateur, and this is only my 4th iPhone screen replacement (have done 5/6 times on iPad as well, since iPad is that mostly used by kids).
Now, all my previous attempts with iPhone 5, 5s, and 6plus has resulted in this very issue; i.e. Proximity sensor not working.
Even for this (i.e. iPhone 6) l faced the same issue. I genuinely hoped this won't happen this time as I had took extra care.
Coming to solution, it took me close to three hours trying various things posted in this forum as well some others.
What it finally worked for me was, GLUE the proximity sensor cabin (sensor was inside that) to the proper place. I know, this might not have worked for some, whereas something else might have, or maybe none had (just as it didn't for me in my previous 3 attempts).
Nonetheless, given that this is an easy solution, and the relief that came along with, I thought to share it over here. Good Luck