Your Firestick runs Fire OS (Android), and Ray's Android app registers as an external video player, so Kodi can hand a video to Ray, which plays it and adds subtitles in 200+ languages.
What you need
A Fire TV Stick
Kodi installed on it
The Ray Android app (APK)
1. Install Ray on the Firestick
The Firestick has no Google Play, so you install Ray from our APK:
On the Firestick: Settings > My Fire TV > Developer options > Install unknown apps, and allow your file app (for example the Downloader app).
Open Downloader and enter the Ray APK link: [your APK download link]
Let it download and install, then open Ray once and sign in.
2. Set Ray as the player in Kodi
In Kodi, find the video you want to watch.
Long-press it (or open its menu) and choose Play using...
Pick Ray from the list.
Kodi hands the video to Ray. Ray opens it, plays it, and you can turn on subtitles in any language from Ray's subtitle menu.
Prefer not to use Kodi?
You can also use the Ray app on its own on the Firestick. Ray's Cinema reads the videos on the device, and plays network links too, with the same subtitles.
Notes
Ray plays standard video files and network streams (including live HLS and DASH).