I store all of my Acid cigars in a separate humidor, as their aroma is pretty strong and will definitely influence other cigars over time.
Naturals are not aromatic or flavored cigars, they just use exotic tobaccos. They can be stored with your more traditional cigars.
Depending on how defined the aroma is from a flavored cigar, I would probably store them separately. However, some flavoreds like CAO seem to focus on taste, rather than aroma, and won't influence your cigars much, if at all. However, I kept my girlfriend's Cojimar's far away from my cigars :)