The fastest way is probably to get a taxi. The cost is about 75 pounds, which split four ways is not bad, and the journey time is 44 mins (though probably a bit more allowing for traffic). For four adults that is actually cheaper than the Heathrow Express.
The next fastest way is to take a taxi from King's Cross to Paddington and then get the Heathrow Express to Heathrow. Taxi fare is going to be about 16 pounds, which split between 4 people is pretty reasonable. The time is about 20 mins for the taxi (add a few minutes of wait time at peak hours), the express time is 15 mins and the max wait for the express is 15 mins, bringing it in at a bit under the hour. However for four adults this will be more expensive than the taxi option. If any of your party are children then that changes things - children travel free on the Heathrow Express.
As Michael Hampton points out, the tube direct on the Piccadilly line is going to be much, much cheaper than any of the above, and only slightly longer. It's likely to clock in at a bit over the hour, after you have got into the underground and waited for the train, and got out again at the end, but its only a few pounds per person, and is undoubtedly the best value for your pound.