Yes :) You can save videos with both embedded and auto-generated subtitles to your computer or iPhone.

1. Enable Subtitles support inside the app.

2. Turn on subtitles support on your iOS device or computer. On your iOS device go to ’Settings’ > ’General’ > ’Accessibility’. On your computer, make sure that your video player supports subtitles.

For your convenience, here’s in-depth guidelines on how to download videos with subtitles on iPhone.