May this will solve your problem.
<Grid x:Name="contentpanel" Grid.Row="1" >
<StackPanel>
<toolkit:AutoCompleteBox x:Name="kk" FilterMode="StartsWith" SelectionChanged="kk_SelectionChanged"/>
</StackPanel>
</Grid>
private void txtFodd_SelectionChanged(object sender, SelectionChangedEventArgs e)
{
if (e.AddedItems.Count == 0)
return;
string mylistItem = (string)e.AddedItems[0];
//Now perform your query with Db with mylistitem string
}