From 6.0.1.41, Jaksta Media Recorder can download and embed Subtitles and Closed Captions, including those automatically generated on YouTube.
JMR will detect, download and embed subtitles if the site has VTT subtitles available and video from the site can be captured using the Video Page Extractor capture method (ie by entering the url of the page hosting the video in the textbox "Enter (or Drag and Drop) the URL of a video page to download", or are otherwise configured in the settings to use the Video Page Extractor when in Auto mode.).
Subtitles can be switched on via Settings > Internet Downloads > Advanced > Page Subtitles.
If downloading subtitles an MP4 file is always generated that contains the video and embedded subtitles.  You can elect to keep the original file that was captured as well as generating an external SRT subtitle format file.
To display Subtitles in Jaksta Media Player, right mouse click the Jaksta Media Player window and select Subtitle and then the embedded Subtitle track.
To display Subtitles in VLC, select the Subtitle menu and then the embedded Subtitle track.