If you have a commercial Whiteboard account, you can duplicate a whiteboard. This duplicate can be used to create new boards or used in a similar fashion to templates. Here is the process you can use:
Go to OneDrive and open My files.
Select the Whiteboard folder to see all your whiteboards.
Choose the board you want to copy as a template.
Click the ... icon.
Click Copy to and then click Copy Here to copy the file to your Whiteboard folder.
You can now open the duplicated whiteboard in OneDrive or the board picker. This will create a new whiteboard with the exact same content that can now be edited and shared.
Personal account users cannot duplicate whiteboard files in OneDrive. To learn more about the differences between commercial and personal accounts, see Differences between Azure and OneDrive for Business whiteboards
Note: The ability to save and share custom templates within the Whiteboard app is coming in a future update.