Hi there Allan and welcome
Its one of the limitations of the App. With an actual Kindle or Kobo you do not need the connection but with the App on an Android device you do sorry.
You best solution is to use Google Books from the Play Store as this you can use offline without the need of an internet connection once the book is downladed
If you would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.