As long as you're signed in with the same Apple ID as used to originally purchase the app, you can install iAnnotate on a new iPad for free (from the "Purchased" section of your App Store app).
However, files stored in the app do not transfer automatically.
With any files/folders contained in cloud connections within the app, you would simply need to make sure everything is up to date (all recent changes uploaded) then create the same connection within iAnnotate on the new iPad.
1. Use the “Send to iTunes” command on each file/folder you want to transfer (make sure you receive a "document updates complete” notification after each attempt)
2. Connect your iPad to your computer and open iTunes File Sharing (iPad > Apps > select iAnnotate from the File Sharing Apps menu)
3. Using the "Save to..." button, save the files/folders you wish to transfer to your desktop and add them into a supported cloud account from there (or if you have a Dropbox/Google Drive desktop app, you can choose to save them directly to the applicable cloud account folder)
4. Create a connection to that cloud account from within iAnnotate on the new iPad and download the files/folders you wish to use