We examine potential observable images of a thin accretion disk surrounding rotating hairy black holes characterized by two non-trivial, time-periodic scalar fields. These black holes provide a viable alternative to the Kerr black hole, with a significantly more complex geodesic structure and resulting accretion disk configurations. We analyze how varying amounts of scalar hair around the black holes, quantified by a normalized charge, influence the direct and indirect images of the accretion disk. Our findings indicate that for the high values of this charge, approaching the boson star limit, the shadow region of the disk images exhibit chaotic patterns with numerous small, disconnected components. For moderately high levels of scalar hair and the associated normalized charge, the shadow region in the images continues to display chaotic characteristics, though a prominent central dark region becomes apparent. At lower normalized charge values, the images of the accretion disk and shadow begin to closely resemble those typical of the Kerr black hole.