There are two ways to move the entries: one is by using iTunes File Sharing, and the other is by using Dropbox.
One way: Using iTunes File Sharing
When you connect your iPhone or iPad to your computer you can open the iTunes application on your computer and browse the contents of the Chronicle folder. If you've created any .backup files, you can see them (and save them to your computer).
Here's how you would move some entries from your iPhone to your iPad using iTunes File Sharing:
Put simply, you're copying the .backup file from your iPhone to your iPad and then importing it.
Another way: Using Dropbox
If you have Chronicle on your iPhone and iPad configured to use your Dropbox account you can easily move .backup files from one device to the other. It's important to configure each app to use the same sub-folder of your Dropbox account (so both copies of the app "see" the same folder). For example, you might have a Dropbox folder named 'chronicle' that both copies of the app are configured to use and store backups in.
This is much easier to do because the app can handle moving the .backup to and from each device via Dropbox. When your copy of Chronicle is configured to use Dropbox, every .backup file you create is automatically uploaded to Dropbox. Likewise, when you browse for .backup files to import on your device, you see ones that are present physically on your device as well as any that are in your Dropbox folder. The app is able to download the files from Dropbox without you having to do anything.