For user saved flights, in the Load Flight window, select a flight and click on the Delete button located under the preview image.

To manually delete, the files are in My Documents>Flight Simulator X Files. Each saved flight is a set of 3 files with a common name and FLT, FSSAVE and WX extensions.

Note: if you should happen to delete your user defined 'Default Flight', the sim will revert to the default-default flight, the Trike over Friday Harbour.