The trekking chefs for the Inca Trail and the many other treks to Machu Picchu are trained since they studied in gastronomy schools in Cusco. There are 2 ways to become a trekking chef and both of them are equally acceptable.
A lot of them study gastronomy, work in the different touristic restaurants Cusco has to offer and then make the jump to the Andes. The other way is by learning on the field. Every trekking chef has an assistant. Someone who will help with all the set up and serving the meals. Learning day by day until the moment he/she is ready to step up as a leading trekking chef. Both ways work and you can find a lot of success stories and joy of being able to work along the treks.
Our trekking chefs are a mix of the two ways. We have amazing chef who started as assistant chefs and even trekking chefs who became leading guides after studying.
Every time you hike the Inca Trail, you are supporting them and also living part of their history.