How to download subtitles for a streaming video?
You need to open "Options→General" IDM dialog and press "Edit" near "Customize IDM Download panels in browsers".
Then press "Add" (arrow 1 on the image) and add SRT (or VTT) file type (arrow 2 on the image). After this play video again and IDM will add download option for subtitles on its video download panel. Please note that subtitles file may have some other file type, it depends on a video.
If do not know what file type is used for subtitles in a video you want to download, try to add "*" as file type. Then IDM will show download options for all requests that are made by a streaming video. Play the video again and look if video download panel has some download option for subtitles. Then you can add file type that has this download option in file types list as it is shown above. Do not forget to uncheck integration for "*" file type.