I just travelled to London and here is my experience. At Heathrow Airport, in Terminal 2, go down to the Underground station and purchase a ticket at the machine; puchase the Travel ticket at a cost of 6 pounds per person. 

You need to take the Picadilly line. This underground train has 25 to 26 stops, and takes about one hour before arriving at King's Cross. There's no need to change trains and it is very easy to take. 

I hope this will help anyone who's going to travel from the airport to King's Cross.