LinkedIn currently does not allow third-party apps, such as CoSchedule, to post a native video to a social message. If you are scheduling to Linkedin, CoSchedule will publish the video as a link hosted by CoSchedule. This video will not auto-play inside of LinkedIn.
If you want to schedule a video that auto-plays on LinkedIn, you may upload your video to a service such as YouTube or Vimeo. Then create a link-type message in CoSchedule and add the video's URL.
The video will then auto-play on LinkedIn's network, but will still look like a link-type message.