If your Screencastify account is connected to your Google Drive (highly recommended), you can grab a link to your recording and share it wherever you'd like.
Copy the Shareable Link
Once you have finished recording, you can select the "Copy Shareable Link" button. The shareable Google Drive link to the recording will automatically be copied to your clipboard.
If your Screencastify account is connected to your Google Drive, all of your recordings will automatically be saved in a folder called "Screencastify" in your Drive.
If you make the entire "Screencastify" folder shareable, then anybody who has a link to that folder will be able to view all of your past and future recordings.
Update Privacy Settings
When you press the "Copy Shareable Link" button, the privacy setting for your video is automatically updated to Unlisted. If you prefer a different privacy setting, simply click "More Options."