Step 1: Head to www.youtube.com
From www.youtube.com, find your video, and click the "Share" button below your video player on the right hand side, highlighted below.
Step 2: Disable Suggested Videos
After clicking "Share", you will want to click on the "Embed" button and uncheck the "video suggestions" box.
Step 3: Copy Your Video URL
After unchecking the box, click "Copy" to copy the URL to your clipboard.
Step 4: Paste Your URL into the "HTML View" of your story editor
Head over your story, open up the HTML view by clicking the (<>) button on the editor toolbar, and paste the link within the code.
Step 5: Preview Your Story
Click on the "View Your Story" link under "Share Your Page" to preview your video on your story.
Step 6: Preview Your Video
Click "Play" and watch your video until the end to check for suggested videos.
Your video should now stop and show the option to replay the video without showing other, suggested videos!