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