You can read a Kindle book via the Kindle app on your Samsung tablet and on your smartphone. The key to syncing across devices is having the Kindle app installed on both.
If you have the Kindle app on both the Samsung Tablet and your Android phone, the library ebook should sync with both as long as the app is registered to the same account on both devices. Here's more information about the Kindle app for Android. (There's lots of good info on this page; scroll down for information on registering your Kindle app).
You can learn more about how to sync your Kindle app across devices here.
