I think seating arrangements are specific to particular airplane models, not flights. Unless you need to display the actual seat layout, a simple list of available seats on each model should suffice. A flight is performed (is that the right word?) by a particular plane model, which determines what seats are initially available. Once a person checks in (this is when the seat is selected) a record is created indicating that a particular seat is occupied on the particular plane model, which is assigned to a particular flight.

Can you tell I have to fly a lot?