Clone this repo, run npm install and gulp build, and in VS Code run the launch as server launch config. This will start the adapter as a server listening on port 4712.
Then in the debuggee, you can add "debugServer": "4712" to connect to your instance of the debug adapter, instead of the installed one. See this page for more details on debugging a debug adapter.
Since most of the code for this extension is in the vscode-chrome-debug-core library, if you need to make changes, then you will probably want to clone both repos. You can run npm link from the vscode-chrome-debug-core directory, and npm link vscode-chrome-debug-core from this directory to make this repo use your cloned version of that library.
See the project under testapp/ for a bunch of test scenarios crammed onto one page.