The web app install banner user prompt that Chrome will trigger to indicate that the user can add your web app to the users home screen. It will only prompt when a number of criteria have been met:
short_name, 144 pixel icon and a type of 'image/png'
The following samples show you the different ways that you can control the Web App banner experience:
Chrome also supports the ability to offer and streamline the install experience of Native Android applications, through the use of 'related_application' data in the manifest.
For testing we encourage you to force the banner to appear by setting the chrome://flags/#bypass-app-banner-engagement-checks flag.