Not so much flavored as customized.
My medium is very drying, which I like immensely. I use it everyday but it has one minor flaw. When I’m painting a large area, my medium is sometimes too drying. One method I use to address this is to add some balsam, like Venice turpentine or Canadian balsam, to my regular distilled turpentine.
In the photo, distilled turpentine from Winsor Newton is on the right. The same turpentine flavored with Venice turpentine is on the left. The untreated turpentine, while not water-clear or as clear as mineral spirits, is pretty clear. The jar on the left was made with 12 ounces of turpentine and a teaspoon of Venice turp. Venice turpentine is very thick and sticky. I hate sticky, gloppy mediums. But in small amounts as used here, it slightly retards drying time without fundamentally transforming the turpentine. The treated turpentine is still a solvent–not a medium.
Sometimes I substitute the flavored turp for regular turp when I mix my medium for the day. Other times, I use regular turpentine to make the medium and use the flavored turp in my solvent cup, which I dip my brush into as needed.
My medium is matte–which I like. I know amateurs and students often like glossy mediums. I think that when they see paintings in museums they attribute the effect of the final varnish to the medium. Anyway, if you use balsams to customize your turpentine as I’ve described, it will impart a slight glossiness to the paint. I do not like that, so I use the customized turp infrequently. But sometimes, it’s perfect for the job.