If you want to search on both FROM and TO airports, you'll want to join on the Airports table twice - then you can use both from and to tables in your results set:
SELECT
Flights.*,fromAirports.*,toAirports.*
FROM
Flights
INNER JOIN
Airports fromAirports on Flights.fairport = fromAirports.code
INNER JOIN
Airports toAirports on Flights.tairport = toAirports.code
WHERE
...