Download your MP4 video and SRT file from YouTube to create a captioned video file that you can share outside of YouTube:
Go to youtube.com and enter the Creator Studio.
To search for a video, select Video Manager, which will display a Search box.
Make sure your video has been captioned. To learn how to caption, See the Captioning tutorial.
In the Edit menu select Download mp4.
Save the video file on your computer.
Return to the Edit menu and select Subtitles.
Because you have already captioned the video you will see the published subtitles listed.
Select the Published subtitles.
Once you have selected the subtitles, the Actions menu will display.
In the Actions menu select SRT and download it onto your computer.
If you would like to incorporate the subtitles into your video see the tutorial, Combining Your Video and Transcript.