There are several ways to copy and save flight plans to create a new flight plan (Check out the videos on our YouTube channel link below). However there is not currently a specific New button in Flightplan to create a file from scratch. The primary reason for this is that the values that define the aircraft, weather, ATC and other game parameters vary widely from one flight plan to another. A New button may be added to future versions of Flightplan (upgrades are free for life).
The recommended method for creating a new flight plan is to first save a flight plan with the desired airports and aircraft using the World Map in Microsoft Flight Simulator 2020 to your local PC and then open it in Flightplan to add/move waypoints or make any other changes. This will ensure that the most current game parameters (including aircraft attributes) are saved to your file. You can then make copies of that file and be confident that the settings for your aircraft are up-to-date (unless an update/mod gets applied). Saving the file in World Map first also ensures that airports are saved with the correct elevations, runways, aprons, parking, etc (if selected).
Airports can be added manually in Flightplan and the aircraft positioned/runway selected in Flightplan https://youtu.be/J4V-ooyVkKw, but World Map has already predefined all runways and parking/apron areas whereas you must know the valid gates/parking to enter yourself in Flightplan. You can change them if you know the exact naming convention for the airport, but it can be helpful to save an airport directly out of World Map at least once with a Gate/Parking selected so that you can see the naming conventions used by looking at the Arrival and Departure Flight Settings (the Gauges Button) in Flightplan. You can then simply change the letter/number combinations to change your gates while keeping any special prefixes/suffixes the particular airport may use (which differ widely).
To create a "new" flight plan from scratch, you can open any flight plan file, save it as another file name on your local PC, then delete all the waypoints/airports and create your own. You can also create a "Discovery" flight out of Flightplan by spawning in-flight.
Check out the How To videos on our YouTube channel for more information https://youtube.com/@simflightplan