I have cookbooks to deploy infrastructure to azure cloud. My cookbooks create required VMs, setup SQL Servers, attach disks to VM and some software installation.
I want that Kitchen CI itself:
If by #1 you mean to check if Chef actually works, don't worry, we have our own test suites for that. What you want focus on is #2, checking that the side effects of your recipes are what you expect. As for how to use Test Kitchen, we have some guides at https://learn.chef.io and the main TK website at https://kitchen.ci/.