Would like to shed some light on this issue as I also have the same problem currently happening on my 5th gen iPad (2017) running latest iOS/Netflix versions.
This contrast/brightness flicker only happens between subtitled dialogues in Netflix films. Within a film, whenever there’s a long pause in dialogue, subtitles won’t be displayed and the top/bottom black bars (due to iPad screen aspect ratio) will normally appear dark. However, whenever dialogue resumes/exists, subtitles will display and there will always be a noticeable shift in contrast where the screen brightness increases slightly, which becomes noticeable against the black bars. I tried producing screenshot to prove this phenomenon, which leads me to the main culprit of this issue, DRM restrictions...
It appears that subtitles are overlaid over the motion picture as a second top layer, which seems to conflict with the contrast of the first layer. Therefore, if a screenshot or screen recording was attempted, only the subtitles would be captured and not the motion picture.
In conclusion, this appears to be a 3rd party issue as it does not affect subtitles from films with the Apple TV app. However, there IS a temporary workaround, and that would be to enable “Smart Invert” from within system Settings > Accessibility > Display & Text Size.
Now if only the Netflix iPad community can report this phenomenon and see what their engineers can do to resolve this issue.