The solution is as simple as that: Bond didn’t fly from Amsterdam, he flew from Frankfurt.
A fellow member from the German Club made an in-depth research on this a few years ago. The scenes were shot in Frankfurt because they couldn’t get a permission to shoot at Amsterdam Schiphol Airport. Lufthansa made it possible for Frankfurt on short notice, but they of course provided a Lufthansa plane for that and not a KLM one. 
The announcement in the movie says it’s coming from Amsterdam, but according to old flight plans, it really started in Frankfurt with just a brief stop over in Amsterdam.
Unfortunately, the hangar where it was shot doesn’t exist any more, but my club fellow located the exact spot so we could go there when we had a club meeting in Frankfurt. It’s not part of the usual airport tour, but once again: the name “James Bond” is able to open many doors 
From Lufthansa archives:
