Would a diet of vitamin water with an occasional flavor packet in water be ok?

That's starvation!: When losing weight you don't "burn body fat" preferentially over muscle. As such, don't waste time or money on fads, products, books, or foods that promise to do so. Strive instead for a realistic goal of 1-2 pounds/week, avoid dehydration (loss of water weight is not meaningful loss), & instead go with fruits, vegetables, whole grains, lean meats, portion-size control, count calories, & exercise.

No. Definitely not: You wouldn't get dehydrated while you are starving. Vitamins only work when taken as part of a (preferably) balanced diet. You need water, protein, carbohydrates, fat, vitamins and minerals. There are over 40 essential nutrients in the diet. The more restricted the diet, the greater the risk of imbalance (hippocrates wrote that 2400 years ago-still true).