Your body can’t make BCAAs on its own, so you need to get them from foods or supplements, whether or not you’re working out. BCAAs are a normal part of the diet, so taking them on rest days shouldn’t be a problem.
One exception is if you have one of the rare conditions that hinder your body’s ability to process BCAAs. A genetic disorder such as maple syrup urine disease prevents the body from metabolising BCAAs due to a lack of a certain enzyme, so it shouldn’t be taken in this instance.