The Divi Code Snippet module lets you display syntax highlighted source code within your Divi Builder pages. If you'd like to include a "Copy Code to Clipboard" button to allow users to quickly and easily copy your code samples, you can do it by setting:

Code Snippet Settings > Code Snippet > Copy-to-Clipboard Button = Yes

Like so:

You can optional also set the tooltip text displayed when the user hovers over the copy-to-clipboard button. 

Here's how the copy button looks on the front-end (with hover tooltip shown):