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The Nazi Flying Wing seen in the film was not a real plane.

 Raiders production designer Norman Reynolds designed the plane for the film, based on historical Northrop Corporation designs and drawings by Ron Cobb of the Horten Ho-2-29.

The fake plane was built by Vickers, and was painted in London at EMI Elstree Studios. In order to ship the unwieldy prop to Tunisia, it had to be disassembled and sent piecemeal before being reconstructed on location.
After the Flying Wing was destroyed in the film in 1981, the remains of the plane sat quietly in the Tunisian desert, where parts of it was salvaged by prop collectors.
http://indianajones.wikia.com/wiki/Flying_Wing
http://dieselpunk.livejournal.com/423162.html#cutid1