This paper presents the flexible RIM Hand, a biomimetic robotic hand that precisely replicates the carpometacarpal (CMC) joints and employs superelastic Nitinol wires throughout its skeletal framework. By modeling the full carpal-to-metacarpal anatomy, the design enables realistic palm deformation through tendon-driven fingers while enhancing joint restoration and supports skeletal structure with Nitinol-based dorsal extensors. A flexible silicone skin further increases contact friction and contact area, enabling stable grasps for diverse objects. Experiments show that the palm can deform up to 28%, matching human hand flexibility, while achieving more than twice the payload capacity and three times the contact area compared to a rigid palm design. The RIM Hand thus offers improved dexterity, compliance, and anthropomorphism, making it promising for prosthetic and service-robot applications.