you need add Microsoft.Phone.Controls.Toolkit nuget package and add the below namespace to your page where you want search box
xmlns:toolkit="clr-namespace:Microsoft.Phone.Controls;assembly=Microsoft.Phone.Controls.Toolkit"
please find the below control paste it in your page and check
<toolkit:PhoneTextBox Background="Gray" VerticalAlignment="Top" BorderThickness="1" Padding="2" BorderBrush="Red" x:Name="txtSearchText" TextWrapping="Wrap" Hint="search here" InputScope="Chat" AcceptsReturn="False" FontSize="21.333" FontFamily="Segoe WP SemiLight" />
hope this helps.
let me know if you it is not working