The combination of camera and lens is important - the faster the focus, the better. That doesn't mean you can't photograph a big bird in flight with entry-level equipment. Rowley advises against using teleconverters so as not to "smudge" the frame and slow down the autofocus system.
Many professional tricks are not about equipment, but about shooting technique. For example, Sam Rowley advises looking through the viewfinder here https://casino-playamo.org/
with two eyes open at once. It's worth limiting the focus range of your lens. If you use a zoom lens, you will find that it only focuses at a certain distance and infinity. This reduces the area that the lens "covers" when focusing and speeds up the shooting process.