Can I have a library eBook on more than one Kindle or Kindle app?
Yes, you can have the same library eBook on more than one Kindle, as long as they are all linked to the same Amazon account.
To do so, access your Amazon account and select Manage your content and devices. Under the tab labeled Your Content, look for the title that you checked out. To the left of the title is a button with 3 dots on it. This is the actions button. Select it to see a menu of possible actions. Choose Deliver to send the book to another Kindle on your account. Choose the Kindle you would like to send it to from the dropdown menu, then select Deliver. If your Kindles remain connected to the Internet at all times, your place in the book will be updated between your devices.
If you do not have WiFi available, you can also choose to download the book and transfer it to your Kindle via USB from the actions menu.