Необходимо указать пространство имен
WITH XMLNAMESPACES ( 'http://schemas.datacontract.org/2004/07/Reaktor.Applikator.DTO' as x)
SELECT tab.col.value('(x:Flag)[1]', 'nvarchar(max)') AS Flag
,tab.col.value('(x:Data/root/root/EmbProd.MonthFee)[1]', 'nvarchar(max)') AS Value
,tab.col.value('(x:ID)[1]', 'nvarchar(max)') AS Product
FROM @xml.nodes('DocumentXML/x:LoadApplicationResult/x:Application/x:EmbeddedProductList/x:EmbeddedProduct') AS Tab(col);