Both destinations are served by Colombo (CMB). Since there's no flight route between them, the best way to travel is by road.
Thiruvananthapuram
Fly to Colombo (CMB), then travel by road to Thiruvananthapuram. Taxis, buses, and private cabs are available from the airport.
Kozhikode
Fly to Colombo (CMB), then travel by road to Kozhikode. Local transport options include taxis, auto-rickshaws, and state buses.