The mammalian auditory system is remarkably adaptable, allowing animals to flexibly respond to sensory information in dynamic environments. Flexible behaviors, such as perceptual learning, involve the engagement of various neural circuits including top-down regions such as frontal areas. However, how multiple brain areas communicate to support learning is unclear. Here, we investigate how frontal and sensory cortical areas interact to enable flexible behavior. We used high-density silicon probes to record single-unit responses simultaneously from auditory cortex (AC), and a downstream region in frontal cortex called secondary motor cortex (M2), while mice performed an auditory reversal learning task. Single-unit responses in both regions were highly diverse, ranging from cells that are highly modulated to sensory stimuli (i.e., classically responsive) to those that appear to fire randomly (non-classically responsive). While classically responsive AC neurons exhibited delayed stimulus responses over learning; in M2 we observed faster stimulus responses, reflecting an unexpected switch in stimulus encoding dynamics from sensory to frontal areas as animals learned to remap stimulus-reward contingencies. Bilateral optogenetic inactivation of M2 inputs impaired reversal learning by preventing the recruitment of non-classically responsive neurons in AC. Population-level decoding revealed that while non-classically responsive cells were preferentially recruited in AC during periods of rapid learning, classically responsive neurons in M2 were recruited during expert performance. Using a dimensionality reduction approach, we found that feedback signals were dominant during rapid learning phases while feedforward signals were dominant during the expert phase of initial task acquisition. These results suggest a dissociable role for diverse neural response types where non-classically responsive cells in AC are critical for enabling flexibility while classically responsive neurons in M2 are important for task-execution once stimulus-reward contingencies have been remapped and the new task rule has been established. Our approach reveals that distinct feedforward and feedback dynamics drive flexible auditory behavior.