Note: while this article is written from the perspective of obtaining Japanese subtitles, it should work just as well for subtitles in other languages.
Update 9/9/18: New version 0.13.12 of the plugin released, should fix login issues.
My journey of obtaining Japanese subtitles from Netflix has been a long one, but I’ve finally arrived at the holy grail: downloading the Japanese subs as TEXT. We had previously discovered that you could download Japanese subtitles as images using a script in your web browser. You could then perform OCR to turn those subtitles into text. While this worked alright, the subtitles weren’t perfect, and would contain some amount of errors that would need to be manually corrected.
This new method is a little more difficult to get set up, but lets you get the subtitles perfectly without any errors. However, there is still one caveat with this method: available subtitles are mostly based on your location. So, this means that MOST Japanese subtitles are only available for people who are physically located in Japan, or who are using one of the few working Japanese VPNs. So the other method of downloading the image-based subtitles might work better for some people, depending on your situation.
I just want the subs!
I have already downloaded Japanese subtitles from over 100 shows and movies, including most native Japanese Netflix originals, and you can grab them all here.
I want to do it myself!
This process involves installing a home theater application called Kodi, and then installing a plugin for it that will allow you to sign into Netflix and then automatically save SRT subtitles for any files videos that you try to play.
The NetflixSubs plugin and installation instructions have been moved to a GitHub page here: https://github.com/Zarxrax/NetflixSubs
Just click through to that page and scroll down for instructions on how to download and install the plugin.
Here is a video tutorial by Matt VS Japan, which shows how to install Kodi and the NetflixSubs plugin, and download subtitles. This uses an older version of the plugin, and some things have changed, but this still gives you a basic overview of how to get things set up.