Here's the solution using Phonegap Build. Add the following to your config.xml to be able to inspect with Chrome Remote Webview Debugging.
First, make sure your widget tag contains xmlns:android="http://schemas.android.com/apk/res/android"
<widget
xmlns="http://www.w3.org/ns/widgets"
xmlns:gap="http://phonegap.com/ns/1.0"
xmlns:android="http://schemas.android.com/apk/res/android"
id="me.app.id"
version="1.0.0">
Then add the following
<gap:config-file platform="android" parent="/manifest">
<application android:debuggable="true" />
</gap:config-file>
It works for me on Nexus 5, Phonegap 3.7.0.
<preference name="phonegap-version" value="3.7.0" />
Build the app in Phonegap Build, install the APK, connect the phone to the USB, enable USB debugging on you phone then visit chrome://inspect.
Source: https://www.genuitec.com/products/gapdebug/learning-center/configuration/