How to create a private chat app with ionic using Firebase or Parse. can anyone suggest good example?
“private” chat app with firebase and parse without encryption and hosted in the usa is a lie!!! 
For a real chatapp you need Sockets. I think there is no BaaS which provides socket connections --> so you need to build your own backend on your own server.
Check this template! 
http://market.ionic.io/plugins/ionic-elastichat-images