In the button's Click event handler you need to call the DataRequested event handler manually. You will not need to send any event args. Please, find an example in our Quick Start Framework:
C:\Program Files (x86)\Telerik\UI for Windows Phone 8 Q2 2015\QSF\Examples.WindowsPhone\DataBoundListBox\OnDemand.xaml
In manual mode, OnListBox_DataRequested is called once on initial load and then it is called from within the button Click event handler.
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