Thameslink operates a train from Crystal Palace to King's Cross Station 4 times a day. Tickets cost $7 - $10 and the journey takes 29 min. Alternatively, London Buses operates a bus from Crystal Palace to King's Cross Station hourly. Tickets cost $3 and the journey takes 45 min.
From Crystal Palace train to London Bridge Underground Station then Tube to King's Cross St. Pancras Underground Station. 31 min £6. From Penge East train to London St Pancras International LL then walk to King's Cross Station. 35 min £6. From Crystal Palace Parade bus to Pentonville, King's Cross Stn York Way. 45 min £2. From Crystal Palace taxi to King's Cross Station. 27 min £45. From Crystal Palace drive to King's Cross Station. 27 min £1. From Crystal Palace Uber to King's Cross Station. 27 min £21.