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