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

It would be best to use the moisturizer in the kit. If it's necessary to use something else, make sure you use a moisturizer that has no fragrance, and is designed for sensitive skin. 

Vi Peel treatments can dry out your skin for a few days. We would recommend the Elevase Moisture Booster after the peels to improve hydration. Elevase contains Opti-Ceramides. Best, DR. Karamanoukian 

Any type of moisturizer for your skin type will work.  The moisturizer that comes in the VI Peel Kit is recommended along with the peel because it has a small amount of hydrocortisone in it to help if there is any irritation.

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.