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