There is no proper way to add buttons that scroll the minimized RadTileViewItems. That is because all items are placed and arranged in a special tileview panel. This means that inserting such buttons will require to write custom panel and re-arrange the items, which won't be an easy task.
Instead, you can use the ScrollBar below the items. Or, you can consider the idea to place the buttons outside of the RadTileView control and update only the scroll position.
However, I think that the RadSlideView in combination with RadListBox will be more suitable for your scenario. I have attached a sample project showing this suggestion. I hope it helps.
Regards,
Martin Ivanov
Progress Telerik
A brand new ThemeBuilder course was just added to the Virtual Classroom. The training course was designed to help you get started with ThemeBuilder for styling Telerik and Kendo UI components for your applications. You can check it out at https://learn.telerik.com