Question [Q] I am stuck at a private shopping list App Idea - Google Cloud Platform

I was writing a simple app for myself that should do the following: Choose some recipes and the app creates a shoppinglist with all the ingredients needed (it adds the amount if something is needed twice ...). The list can be used while shopping and the ingredients can be swiped off the list (if you bought them) So far it works perfectly.

The next step I want to take with the app, and the point were I stuck for days now is the following idea: I want to share the list with another device (only one) so we can go shopping together and if someone swipes out one ingredient it synchronises with the other ones app.

I tried to achives this by using the Google Cloud Platform (http://googlecloudplatform.blogspot....studio_26.html) but somehow i cant get it to work.
And for some reason I start asking myself if this is even possible to do it this way (for free).
Does anyone has and idea if this is possible? And can someone maybe give me a small hint how to achive this?