Do I use data when I read on my kindle app on my iPad

You should only use data when you download the book. As I understand it your book is on your device and you read it from there. The only data usage I can think of is if you are doing their 'sync your book across your devices' then Device one would have to tell Device two 'she's on page 49 now'

Go to usage and check the Kindle app to see it's data usage.

And I believe the thing "phones home" at the start or restart of a session to make sure you're still entitled to peruse the goods. But that would be a brief burst of data.