There are two ways to style the ComboBox in the Filtering Flyout:
You can explicitly define a custom style in the resources of the RadDataGrid. I have attached a sample application that uses the default style of that element - you can paste it in your code and customize it with your own brushes. Note that you have to add an instance of the PaletteInitializer class to your page resources before you can use the predefined Telerik brushes.
You can globally change the style of all ComboBoxes in your application by defining custom resource in the App.xaml file, for example: