From this page ->Using Kindle for iPad/iPhone/iPod touch
Removing Content from the Kindle Application
The Kindle application allows you to remove individual items from your iPad, iPhone or iPod touch so you don't have to use your device's memory to store all of your reading material. See Downloading Archived Items to the Kindle Application for information about accessing your Kindle Library on Amazon.com.
To remove individual items from the Home screen:
For the iPhone and iPod touch:
Tap the desired title and slide your finger to the right to reveal the Archive or Delete button. Content that is purchased from the Kindle Store is archived and can be re-downloaded at any time; sideloaded content is permanently deleted. Then tap the Archive or Delete button next to the title.
For the iPad:
In cover view: Tap Press on the icon cover for the title and hold it until the "X" appears on the cover. Then tap on the "X" to finish deleting the title.
In List view: Swipe your finger across the title toward the left to display the Archive or Delete button. Content that is purchased from the Kindle Store is archived and can be re-downloaded at any time; sideloaded content is permanently deleted. Tap Archive or Delete to remove the book from your Home screen. Archived content will remain in your Archived Items.
To delete all content by uninstalling the application:
- Visit the device's Home screen by pressing the Home button on your iPad, iPhone or iPod Touch.
- Tap and hold the Kindle icon until the icons start to shake.
- Tap the "X" icon on the upper left-hand corner of the icon.
- Tap the Delete button to remove the application and its contents.
Removing Kindle content from the Kindle application or uninstalling the application does not remove purchased items from your Kindle Library stored on Amazon.com. You'll still be able to redownload your content to registered devices from www.amazon.com/manageyourkindle.