When user click or touch the button, the application will randomly pick a number from user's phone contact list and call. I see this kind of app from google play store but I was wondering if it is possible to create one like this with flutter?
If yes, are there any resources I can look into? Thanks in advance
Yes, it's possible.
You can look in pub.dev, the official package repository for Dart and Flutter apps. Search for "get phone contact". Pick one package, then use it to get the contact list.
Google "dart get random element from list" and click the first stack overflow link you see.