Direct trains from Dover Priory to Edinburgh Waverley take about 5 hours 30 minutes. Operated by First Great Western and Southeastern; ~10 daily. Fares: ~£99 standard, £159 first class.
Journey around 11 hours 40 minutes; average ticket £41.
Drive ~450 miles via A1 and A68; roughly 7 hours.
No direct flights from Dover. Fly from London Stansted (~2 hours from Dover by car) to Edinburgh in ~2 hours 35 minutes.