I want to travel from Santiago (Chile) to Lima (Peru). I will not go through Bolivia but I would like to visit the salt flats from the Chilean side. Is this possible? I only want to hop over to the Bolivian salt flats and back. I've heard that the salt flats in Bolivia are really worthwhile so I might want to skip the ones in Chile.
It will depend on how much time you have. Salar de Uyuni is HUGE (10,582 square kilometers), and not only you will need time to get there, but also to see the many different facets of it.
Still, it is possible to visit it from Chile if you have enough time. You can get a train from Avaroa on the Chilean border, but keep in mind the schedule is not exactly trustworthy and times can vary a lot. Also, because you are crossing a border, you will need some extra time for the paperwork.
The best option would be, in my opinion, a tour from for example San Pedro de Atacama. Tours can last up to five days, and they usually include Laguna colorada (a beautiful red lake full of flamingos), the geysers (when I went to had to depart at 5 am to see them, the sunrise is beautiful) and Tupiza (giant columns of clay). They also tend to include delicious meals, (very humble) accomodation and a guide.
I strongly recommend you do it if you have time. It's a unique place, full of unexpected marvels. If you are going to be there overnight, be careful with the temperature changes. At night it can descend drastically (we are talking about -10 or so in the winter), and during the day it's quite hot. Also, don't forget your sunglasses, as the glare can be quite strong.