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Possible.
Is the app up to date? The last update was about two weeks ago.
Make sure your device is connected to Wi-Fi, and take a look at your payment method.
Try syncing your device: go to the Home screen in the Kindle app, tap the Menu icon at the top right, and select “Sync”.
Also make sure your filter (top left on the Home screen in Kindle) isn’t set to something that doesn’t show samples.