Several muscles are involved in moving the forearm and hand, but none of them specifically supinate the hand and flex the forearm. The brachoradialis muscle comes closest to this, as it is able to flex, semi-supinate and semi-pronate the forearm. The hand is supinated by the supinator muscle.
Several muscles are able to flex the forearm, either as their primary function or as an effect of their work on the upper arm. These flexor muscles are the biceps brachii, the brachialis, the brachoradialis and the pronator teres. The hand is supinated only by the supinator muscle, which is attached to the wrist and elbow.