I have created a small app where my mobile visitors could message WhatsApp users without saving their numbers in the contact list (test link)
No matter what I try, I am unable to get the "Add to Homescreen" prompt displayed when a mobile user visits this website.
Chrome Dev tool says "Site cannot be installed: the page does not work offline". How do I solve this issue?
If you refer to the Add to Home Screen page at Google Developers, you will notice it asks to make sure your service worker is registered to accept the 'fetch' event before it will display the add to home screen prompt.
For your application, that is not the case. Make sure to add that event and test that your application will perform as expected when offline, even if that just means an error page. Here is a good page and section to reference to get started.