Openflights has long been the tool many of us use to log their flights, but it has two big problems:
1 - You can't add new airlines, so my recent flights on ITA Airways and Breeze, for example, can't be logged as such.
2 - The "List flights" function currently appears to be broken. It lists flights only partially.
1/ I think you can, airlines, airports - I checked their FAQ/help not long ago because of this and there's a way to do it (
https://openflights.org/help/airline)
2/ my flights seem to list correctly