Background image in a polygon / CountryData

This example is from the documentation for Texture in Mathematica version 8:

With[{vc = 
 Transpose[
  Rescale /@ Transpose[First[CountryData[#, "Coordinates"]]]]}, 
Show[CountryData[#, "Shape"], 
 ImageSize -> {{100}, {100}}] /. {RGBColor[__] :> 
  Texture[ImageReflect[Image[CountryData[#, "Flag"]], 
    Top -> Right]], 
 Polygon[a_] :> 
  Polygon[First[a], VertexTextureCoordinates -> vc]}] & /@ 
CountryData["SouthAmerica"]

but I don't know whether it does what you need. Still, it looks pretty.

Try:

Graphics[{EdgeForm[White], {{Texture[Image[CountryData[#, "Flag"]]], 
  Polygon[First@First[CountryData[#, "Polygon"]], 
   VertexTextureCoordinates ->Transpose[
     Rescale /@ Transpose[First@First[CountryData[#, 
         "Polygon"]]]]]}} & /@ {"Venezuela", "Colombia"}}]

which gives