Massage can fit either before or after a flight, but the better timing depends on what you want from the session. Before travel, the goal may be relaxation. After travel, it may be general comfort after sitting and carrying luggage.
Massage before a flight
A pre-flight session can be convenient if you are not rushing to the airport. Leave enough time to shower, eat, hydrate and travel without turning the massage into another deadline.
Massage after a flight
After landing, a gentle relaxation session may feel comfortable once you have eaten, hydrated and settled. Avoid using massage to push through severe pain, unexplained swelling, fever or injury.
Long flights require extra caution with swelling
One-sided leg swelling, chest pain or shortness of breath after prolonged travel can be warning signs that require medical attention, not massage.
Choose the option that reduces stress
If a massage before departure makes your airport schedule tighter, it may defeat the purpose. If you arrive exhausted late at night, sleep may be the higher priority.
See also how to recover after a long flight.