Every recording you make will automatically be saved to your Google Drive in a folder called "Screencastify" once your video has been created. You can then open the Video Management Page for that video to grab the Drive link for that video.
On the Video Management Page, you can click on "Google Drive" : 
then copy the 'Copy Drive Link' : 
You will also have options on the share settings you wish to set for that video!
This process could take a few minutes, depending on how long your recording is.
Important: if you delete a recording on your Video Management Page, it will also be deleted from your Drive and your My Recordings folder. If you move a video out of "Screencastify" folder in your Drive, you will no longer see it in My Recordings in Screencastify.
NOTE
Your recording may appear blurry in your Google Drive immediately after uploading because Google processes the low-res version first. The full-resolution version of your video will be available within 15 minutes.
What's Next? 🧐
Learn about the three different ways to share a recording: