gatwick to edinburgh

If your flight arrive at 06:40, you will need average one hour to go through custom and reclaim your luggage. Then you have approximately 2 hours to check in easy-jet flight to Edinburgh, which should be enough.

Both Oasis and Easyjet are at Gatwick South terminal. So you should not need to travel too far. As soon as you get your luggages, you will have to travel from arrival floor to departure floor to easyjet check in counter.

Gatwick Airport Terminal Information

Destination Airline / Tour Operator Terminal Code Telephone No.
Hong Kong Oasis Hong Kong Airlines South O8
Edinburgh easyJet South EZY

Unless the flight delay for 90 minutes, I think you should still be able to make it. Unfortunately, the next flight for easyjet or BA are 14:20. So will have to take a risk.
Otherwise, you will have to travel to Heathrow or Central London to take trains.

Good Luck