Coexistence of phases, characterized by different electronic degrees of freedom, commonly occurs in layered superconductors. Among them, alkaline intercalated chalcogenides are model systems showing microscale coexistence of paramagnetic (PAR) and antiferromagnetic (AFM) phases, however, temporal behavior of different phases is still unknown. Here, we report the first visualization of the atomic motion in the granular phase of K$_{x}$Fe$_{2-y}$Se$_2$ using X-ray photon correlation spectroscopy. Unlike the PAR phase, the AFM texture reveals an intermittent dynamics with avalanches as in martensites. When cooled down across the superconducting transition temperature T$_c$, the AFM phase goes through an anomalous slowing behavior suggesting a direct relationship between the atomic motions in the AFM phase and the superconductivity. In addition of providing a compelling evidence of avalanche-like dynamics in a layered superconductor, the results provide a basis for new theoretical models to describe quantum states in inhomogeneous solids.
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