What kind of moisturizer can I use after the VI Peel other than the one that comes in the kit?

The two most important things after any chemical peel are bland emolliation (moisturization, hydration) and sun avoidance.  I would recommend that you use something bland and gentle such as aquaphor ointment, Cetaphil Daily Facial Moisturizer or Cerave Facial Moisturizing Lotion (AM or PM).  Until the healing is over, I would avoid any products with retinol, salicylic acid, glycolic acid or benzoyl peroxide acid as they will likely irritate your skin.  Make sure to gently cleanse and to avoid picking at peeling skin.  If you have persistent redness and/or itching, you can speak with your doctor about the possibility of using a topical hydrocortisone lotion for the peeled areas.