This looks like a many to many relationship to me. A passenger can go on many flights and a flight can list many passengers.
Start with these relationships:
Passengers::__pkPassengerID = Passenger_Flight::_fkPassengerID
Flights::__pkFlightID = Passenger_Flight::_fkFlightID
You can place a portal to Passenger_Flight on the Passengers layout to list and select Flights records for each given Passengers record. Fields from Flights can be included in the Portal to show additional info about each selected Flights record and the _fkFlightID field can be set up with a value list for selecting Flights records by their ID field.
Many thanks for pointing me in the right direction. I am still trying to get it to work but will need a little more time.
Here's a demo file you may find to be a good source of ideas for working with a many to many relationship: https://www.dropbox.com/s/oyir7cs0yxmbn6i/ManyToManywDemoWExtras.fp7
If you are using FileMaker 12 or newer, use Open from FileMaker's file menu to open the file and thus produce a copy converted over to the .fmp12 file format.
Thank you, most kind and very helpful.