Greetings, Charlie, welcome to the forums!
You can certainly use ExpressionEngine to store this data - you would have one weblog to hold all of your flight details, and another weblog to hold your airport and airline data. You would then relate the two using entry relationships.
All of that is available out of the box.
The tricky part here, however, is going to be importing your existing data. You can import using the MT Import Format or CSV Grab; the former does not support relationships, and I am not sure if the latter does. This may need to be some custom import work. If you need assistance with that, you might consider a post on the Job Board or working with one of our Pro Net members.
I would strongly recommend trying out EE and if you like it, then peruse the import options.