A convenient way to get from Earls Court (actually West Brompton) to Gatwick is the easyBus which can be as low as £2 when booked online in advance - but if your arriving flight is delayed there may be trouble. If you arrive earlier than your booked time and there are seats, the driver will try to fill up the van

Alternatively the way that I do it is to take the Overground from West Brompton to Clapham Junction, and change to a Southern train that goes to Gatwick. This is easier than changing at Victoria, but you can't buy rail tickets at West Brompton which means you'll have to buy them online and collect at a different station. (Or use an Oyster, exit the system at East Croydon and re-enter with a paper ticket...)