No, you should not use Resolve on velvet.
Based on the Resolve® Easy Clean Brushing Kit instructions, it is explicitly stated that you should not use it on velvet. The kit is designed for use on area rugs and carpets made of materials like wool, nylon, acrylic, and stain-resistant carpet. Using it on velvet could damage the fabric or affect its color.
The general recommendation is to avoid using this particular Resolve product on delicate materials like velvet, silk, leather, vinyl, or cotton.