you could use the flights API to create your own callsign/origin/destination database. This data is based on an analysis of flights in the past and will work in areas only where OpenSky Network has a good coverage at low altitudes to detect the departure and arrival airport.
Another option is to use a downloadable database like that from the Virtual Radar Server project (www.virtualradarserver.co.uk/FlightRoutes.aspx).
Or you could utilise airport APIs providing a mapping from callsigns to flight numbers and flight routes (see apideveloper.swedavia.se and developer.finavia.fi for Swedish and Finnish public airports). Many other public data sources contain the flight number only and not the callsign. Many callsigns include the flight number if there is not an alphanumerical suffix after the operator ICAO id.