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