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