I called the Starbucks info line 1-800-23LATTE to find out if their new smoothie-like product the Vivanno has gluten. One of their customer service reps told me that it is gluten free - I didn't ask what was in the fiber powder, but at least I know it's not wheat.
A commenter on this post reports "There is a possible cross-contamination issue with the protein and fiber powder for the Vivanno drinks." - So if you want to be super safe, ask them not to put the powder in the drink.
Also, the Starbucks representative reminded me that all of the Starbucks beverages are Gluten Free except for Frappuccinos with chocolate chips and any blended beverage using the Vanilla Bean Powder.