There is many ways to hold a tournament.
If you wants a easy way you just let the players meet each other 2 and 2, the living one will meet the next oponent and so on. Have the players randomly use a side and a plane in about the same class.Or you can have 4 players playing until 2 are dead every round. In any ways should death mean that the player is out of the tournament.
Or do you mean a campaign? In that case it is the side who wins and not a single player.That is a lot more interesting in my book.
Then you first choose how many games you should play and when. Our campaign is one game every month from feb 1916 to nov 1918 but that is kinda a long one.
Then you decide on scenarios and what each side needs to be doing to win that scenario. You could have a whole list and have each side draw one randomly or you could make them based on events in the war or just what you think is fun. Stuff like artillery plotting, baloon bursting and so on.
Then you decide if the pilots should get experience if the survive, and what experience can give them. There are several threads about it here and some webbpages with ideas for this.
Then you choose which planes the players could choose from. You could make a system where the player gets a cooler plane depending on how much experience he have. We put in a certain number of new planes every month and if one side loses a lot they will have to use older planes, the experienced players gets first pick.
Then just play and record who wins the scenarios and individual points to see which pilot that did best.